TY - JOUR AU - Abdellaoui, Boumediene AU - Peral, Ireneo AU - Primo, Ana AU - Soria, Fernando TI - On the KPZ equation with fractional diffusion: Global regularity and existence results JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 312 PY - 2022 SP - 65 EP - 147 PG - 83 SN - 0022-0396 DO - 10.1016/j.jde.2021.12.016 UR - https://m2.mtmt.hu/api/publication/32931156 ID - 32931156 AB - In this work we analyze the existence of solutions to the fractional quasilinear problem,(P) {u(t) + (-Delta)(s) u = vertical bar del vertical bar(alpha) + f in Omega(T) equivalent to Omega x (0, T),u(x, t) = 0 in (R-N \ Omega) x [0, T),u(x, 0) = u(0)(x) in Omega,where Omega is a C-1,C-1 bounded domain in R-N, N > 2s and 1/2 < s< 1. We will assume that fand u(0) are non negative functions satisfying some additional hypotheses that will be specified later on.Assuming certain regularity on f, we will prove the existence of a solution to problem (P) for values a < s/1-s, as well as the non existence of such a solution when alpha > 1/1-s. This behavior clearly exhibits a deep difference with the local case. (c) 2021 Elsevier Inc. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Lu, Heqian AU - Zhang, Zhengce TI - The Cauchy problem for a parabolic p-Laplacian equation with combined nonlinearities JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 514 PY - 2022 IS - 2 PG - 40 SN - 0022-247X DO - 10.1016/j.jmaa.2022.126329 UR - https://m2.mtmt.hu/api/publication/33161235 ID - 33161235 AB - This article studies the Cauchy problem for the evolution p-Laplacian equation u(t) - Delta(p)u = lambda(u)m + mu vertical bar del u vertical bar(q)u(r) in R-N x (0, T). The local existence, global existence and nonexistence of solutions are investigated. In particular, for the case lambda > 0 and mu > 0, we obtain an optimal Fujita-type result, which demonstrates the positive gradient term brings about the discontinuity phenomenon of the critical exponent. For the case lambda > 0 and mu < 0, the existence and nonexistence of global solutions are also discussed. (C) 2022 Elsevier Inc. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Liang, Mengyang AU - Fang, Zhong Bo AU - Yi, Su-Cheol TI - Blow-up analysis for a reaction-diffusion equation with gradient absorption terms JF - AIMS MATHEMATICS J2 - AIMS MATH VL - 6 PY - 2021 IS - 12 SP - 13774 EP - 13796 PG - 23 SN - 2473-6988 DO - 10.3934/math.2021800 UR - https://m2.mtmt.hu/api/publication/32931157 ID - 32931157 AB - This paper deals with the blow-up phenomena of solution to a reaction-diffusion equation with gradient absorption terms under nonlinear boundary flux. Based on the technique of modified differential inequality and comparison principle, we establish some conditions on nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, some bounds for blow-up time are derived under appropriate measure in higher dimensional spaces (N >= 2). LA - English DB - MTMT ER - TY - JOUR AU - Liang, Mengyang AU - Fang, Zhong Bo TI - Blow-Up Phenomenon for a Reaction-Diffusion Equation with Weighted Nonlocal Gradient Absorption Terms JF - MEDITERRANEAN JOURNAL OF MATHEMATICS J2 - MEDITERR J MATH VL - 18 PY - 2021 IS - 4 PG - 19 SN - 1660-5446 DO - 10.1007/s00009-021-01795-5 UR - https://m2.mtmt.hu/api/publication/32292377 ID - 32292377 AB - This paper deals with the blow-up phenomenon of solutions to a reaction-diffusion equation with weighted nonlocal gradient absorption terms in a bounded domain. Based on the method of auxiliary function and the technique of modified differential inequality, we establish appropriate conditions on weight function and nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, upper and lower bounds for blow-up time are derived under appropriate measure in higher dimensional spaces. LA - English DB - MTMT ER - TY - JOUR AU - Li, Tian-Hong AU - Wang, Jinghua AU - Wen, Hairui TI - Regularity and global structure for Hamilton-Jacobi equations with convex Hamiltonian JF - JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS J2 - J HYPERBOL DIFFER EQ VL - 18 PY - 2021 IS - 02 SP - 435 EP - 451 PG - 17 SN - 0219-8916 DO - 10.1142/S0219891621500132 UR - https://m2.mtmt.hu/api/publication/32292378 ID - 32292378 AB - We consider the multidimensional Hamilton-Jacobi (HJ) equation u(t)+gamma(-1)vertical bar Du vertical bar(gamma) = 0 with 1 < gamma < 2 being a constant and for bounded C-2 initial data. When gamma = 2, this is the typical case of interest with a uniformly convex Hamiltonian. When gamma = 1, this is the famous Eikonal equation from geometric optics, the Hamiltonian being Lipschitz continuous with homogeneity 1. We intend to fill the gap in between these two cases. When 1 < gamma < 2, the Hamiltonian H(p) = gamma(-1)vertical bar p vertical bar(gamma) is not uniformly convex and is only C1 in any neighborhood of 0, which causes new difficulties. In particular, points on characteristics emanating from points with vanishing gradient of the initial data could be "bad" points, so the singular set is more complicated than what is observed in the case gamma = 2. We establish here the regularity of solutions and the global structure of the singular set from a topological standpoint: the solution inherits the regularity of the initial data in the complement of the singular set and there is a one-to-one correspondence between the connected components of the singular set and the path-connected components of the set {y(0)vertical bar g(y(0)) >inf(y)is an element of R-n g(y)}. LA - English DB - MTMT ER - TY - JOUR AU - Meinlschmidt, Hannes AU - Rehberg, Joachim TI - Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 280 PY - 2021 SP - 375 EP - 404 PG - 30 SN - 0022-0396 DO - 10.1016/j.jde.2021.01.032 UR - https://m2.mtmt.hu/api/publication/32292379 ID - 32292379 AB - In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolev-type spaces of negative order X-D(s-1,q) (Omega) for s > 0 small, including mixed boundary conditions and with a fully nonsmooth geometry of Omega and the Dirichlet boundary part D. We expect the result to find applications in the analysis of nonlinear parabolic equations, in particular for quasilinear problems or when treating coupled systems of equations. To demonstrate the usefulness of our result, we give a new proof of local-in-time existence and uniqueness for the van Roosbroeck system for semiconductor devices which is much simpler than already established proofs. (C) 2021 Elsevier Inc. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Mohammed, Benlahsen AU - Vadászné Bognár, Gabriella AU - Csáti, Zoltán AU - Guedda, Mohammed AU - Hriczó, Krisztián TI - Dynamical properties of a nonlinear Kuramoto–Sivashinsky growth equation JF - ALEXANDRIA ENGINEERING JOURNAL J2 - ALEX ENG J VL - 60 PY - 2021 IS - 3 SP - 3419 SN - 1110-0168 DO - 10.1016/j.aej.2021.02.003 UR - https://m2.mtmt.hu/api/publication/31883568 ID - 31883568 LA - English DB - MTMT ER - TY - JOUR AU - Abdellaoui, B. AU - Attar, A. AU - Bentifour, R. AU - Laamri, E-H TI - Existence Results to a Class of Nonlinear Parabolic Systems Involving Potential and Gradient Terms JF - MEDITERRANEAN JOURNAL OF MATHEMATICS J2 - MEDITERR J MATH VL - 17 PY - 2020 IS - 4 PG - 30 SN - 1660-5446 DO - 10.1007/s00009-020-01542-2 UR - https://m2.mtmt.hu/api/publication/31416523 ID - 31416523 AB - In this paper, we investigate the existence of solutions to a nonlinear parabolic system, which couples a non-homogeneous reaction-diffusion-type equation and a non-homogeneous viscous Hamilton-Jacobi one. The initial data and right-hand sides satisfy suitable integrability conditions and non-negative. To simplify the presentation of our results, we will consider separately two simplified models : first, vanishing initial data, and then, vanishing right-hand sides. LA - English DB - MTMT ER - TY - JOUR AU - Abdellaoui, M. TI - Asymptotic behavior of solutions for nonlinear parabolic operators with natural growth term and measure data JF - JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS J2 - J PSEUDO-DIFFER OPER VL - 11 PY - 2020 IS - 3 SP - 1289 EP - 1329 PG - 41 SN - 1662-9981 DO - 10.1007/s11868-019-00324-z UR - https://m2.mtmt.hu/api/publication/31416525 ID - 31416525 AB - We are interested in the asymptotic behavior, as t tends to +infinity, of finite energy solutions and entropy solutions u(n) of nonlinear parabolic problems whose model is{u(t) - Delta(p)u + g(u)vertical bar del vertical bar(p) = mu in (0, T) x Omega, u(0,x) = u(0)(x) in Omega, u(t,x) = 0 on (0,T) x partial derivative Omega (0,1)where Omega subset of R-N is a bounded open set, N >= 3, u(0) is an element of L-1(Omega) is a nonnegative initial data, whileg: R -> R is a real function in C-1(R) which satisfies sign condition with positive derivative and mu is a nonnegative measure independent on time which does not charge sets of nullp-capacity. LA - English DB - MTMT ER - TY - JOUR AU - Esteve, Carlos TI - Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equation in domains with non-constant curvature JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES J2 - J MATH PURE APPL VL - 137 PY - 2020 SP - 143 EP - 177 PG - 35 SN - 0021-7824 DO - 10.1016/j.matpur.2019.12.006 UR - https://m2.mtmt.hu/api/publication/31416522 ID - 31416522 AB - We consider the diffusive Hamilton-Jacobi equation ut - Delta u =vertical bar del u vertical bar(p) in a bounded planar domain with zero Dirichlet boundary condition. It is known that, for p > 2, the solutions to this problem can exhibit gradient blow-up (GBU) at the boundary. In this paper we study the possibility of the GBU set being reduced to a single point. In a previous work [Y.-X. Li, Ph. Souplet, 2009], it was shown that single point GBU solutions can be constructed in very particular domains, i.e. locally flat domains and disks. Here, we prove the existence of single point GBU solutions in a large class of domains, for which the curvature of the boundary may be nonconstant near the GBU point.Our strategy is to use a boundary-fitted curvilinear coordinate system, combined with suitable auxiliary functions and appropriate monotonicity properties of the solution. The derivation and analysis of the parabolic equations satisfied by the auxiliary functions necessitate long and technical calculations involving boundaryfitted coordinates. (C) 2019 Elsevier Masson SAS. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Jleli, Mohamed AU - Samet, Bessem AU - Souplet, Philippe TI - DISCONTINUOUS CRITICAL FUJITA EXPONENTS FOR THE HEAT EQUATION WITH COMBINED NONLINEARITIES JF - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - P AM MATH SOC VL - 148 PY - 2020 IS - 6 SP - 2579 EP - 2593 PG - 15 SN - 0002-9939 DO - 10.1090/proc/14953 UR - https://m2.mtmt.hu/api/publication/31416524 ID - 31416524 AB - We consider the nonlinear heat equation u(t) - Delta u = vertical bar u vertical bar(p)+b vertical bar del u vertical bar(q) in (0,infinity) x R-n, where n >= 1, p > 1, q >= 1, and b > 0. First, we focus our attention on positive solutions and obtain an optimal Fujita-type result: any positive solution blows up in finite time if p <= 1+ 2/n or q <= 1+ 1/n+1, while global classical positive solutions exist for suitably small initial data when p > 1 + 2/n and q > 1+ 1/n+1. Although finite time blow-up cannot be produced by the gradient term alone and should be considered as an effect of the source term vertical bar u vertical bar(p), this result shows that the gradient term induces an interesting phenomenon of discontinuity of the critical Fujita exponent, jumping from p = 1+ 2/n to p = infinity as q reaches the value 1 + 1/n+1 from above. Next, we investigate the case of sign-changing solutions and show that if p <= 1 + 2/n or 0 < (q - 1)(np - 1) <= 1, then the solution blows up in finite time for any nontrivial initial data with nonnegative mean. Finally, a Fujita-type result, with a different critical exponent, is obtained for sign-changing solutions to the inhomogeneous version of this problem. LA - English DB - MTMT ER - TY - JOUR AU - Shan, M. A. AU - Skrypnik, I. I. TI - Keller-Osserman estimates and removability result for the anisotropic porous medium equation with gradient absorption term JF - MATHEMATISCHE NACHRICHTEN J2 - MATH NACHR VL - 292 PY - 2019 IS - 2 SP - 436 EP - 453 PG - 18 SN - 0025-584X DO - 10.1002/mana.201700177 UR - https://m2.mtmt.hu/api/publication/30901957 ID - 30901957 AB - We study "large" nonnegative solutions for a class of quasilinear equations model of which isu(t) - Sigma(n)(i=1)(u(mt-1)u(xt))(xt) + Sigma(n)(i=1)vertical bar u(xt)vertical bar(qt) = 0.We give a sufficient condition on the exponents m(i) and q(i) for the removability of isolated singularities. LA - English DB - MTMT ER - TY - JOUR AU - Ma, Lingwei AU - Fang, Zhong Bo TI - Bounds for blow-up time of a reaction-diffusion equation with weighted gradient nonlinearity JF - COMPUTERS AND MATHEMATICS WITH APPLICATIONS J2 - COMPUT MATH APPL VL - 76 PY - 2018 IS - 3 SP - 508 EP - 519 PG - 12 SN - 0898-1221 DO - 10.1016/j.camwa.2018.04.033 UR - https://m2.mtmt.hu/api/publication/30462863 ID - 30462863 AB - In this paper, we focus on the bounds for blow-up time of null Dirichlet initial boundary value problem for a reaction-diffusion equation with weighted gradient nonlinearity. By virtue of the method of super-sub solution and the technique of modified differential inequality, we establish sufficient conditions to guarantee that the solution blows up at finite time under appropriate measure sense. Meanwhile, upper and lower bounds for the blow-up time are found in higher dimensional spaces and some examples for application are presented. (C)2018 Elsevier Ltd. All rights reserved . LA - English DB - MTMT ER - TY - CHAP AU - Peral, Ireneo ED - Valdinoci, E ED - Farina, A TI - On Some Elliptic and Parabolic Equations Related to Growth Models T2 - PARTIAL DIFFERENTIAL EQUATIONS AND GEOMETRIC MEASURE THEORY PB - Springer Netherlands CY - Cham (Németország) T3 - Lecture Notes in Mathematics, ISSN 0075-8434 PY - 2018 SP - 43 EP - 195 PG - 153 DO - 10.1007/978-3-319-74042-3_2 UR - https://m2.mtmt.hu/api/publication/30462861 ID - 30462861 LA - English DB - MTMT ER - TY - JOUR AU - Cosso, Andrea AU - Huyen, Pham AU - Xing, Hao TI - BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data JF - ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES J2 - ANN I H POINCARE-PR VL - 53 PY - 2017 IS - 4 SP - 1528 EP - 1547 PG - 20 SN - 0246-0203 DO - 10.1214/16-AIHP762 UR - https://m2.mtmt.hu/api/publication/27060264 ID - 27060264 LA - English DB - MTMT ER - TY - JOUR AU - Iagar, Razvan Gabriel AU - Laurencot, Philippe AU - Stinner, Christian TI - Instantaneous shrinking and single point extinction for viscous Hamilton-Jacobi equations with fast diffusion JF - MATHEMATISCHE ANNALEN J2 - MATH ANN VL - 368 PY - 2017 IS - 1-2 SP - 65 EP - 109 PG - 45 SN - 0025-5831 DO - 10.1007/s00208-016-1408-z UR - https://m2.mtmt.hu/api/publication/26732933 ID - 26732933 LA - English DB - MTMT ER - TY - JOUR AU - Iagar, Razvan Gabriel AU - Laurencot, Philippe TI - Large Time Behavior for a Quasilinear Diffusion Equation with Critical Gradient Absorption JF - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS J2 - J DYN DIFFER EQU VL - 29 PY - 2017 IS - 3 SP - 817 EP - 832 PG - 16 SN - 1040-7294 DO - 10.1007/s10884-015-9508-0 UR - https://m2.mtmt.hu/api/publication/26889889 ID - 26889889 LA - English DB - MTMT ER - TY - JOUR AU - Iagar, Razvan Gabriel AU - Laurencot, Philippe TI - Self-similar extinction for a diffusive Hamilton-Jacobi equation with critical absorption JF - CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS J2 - CALC VAR PARTIAL DIF VL - 56 PY - 2017 IS - 3 PG - 38 SN - 0944-2669 DO - 10.1007/s00526-017-1158-0 UR - https://m2.mtmt.hu/api/publication/26712965 ID - 26712965 LA - English DB - MTMT ER - TY - JOUR AU - Iwabuchi, Tsukasa AU - Kawakami, Tatsuki TI - Existence of mild solutions for a Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES J2 - J MATH PURE APPL VL - 107 PY - 2017 IS - 4 SP - 464 EP - 489 PG - 26 SN - 0021-7824 DO - 10.1016/j.matpur.2016.07.007 UR - https://m2.mtmt.hu/api/publication/26712967 ID - 26712967 LA - English DB - MTMT ER - TY - JOUR AU - Porretta, Alessio AU - Souplet, Philippe TI - The Profile of Boundary Gradient Blowup for the Diffusive Hamilton-Jacobi Equation JF - INTERNATIONAL MATHEMATICS RESEARCH NOTICES J2 - INT MATH RES NOTICES PY - 2017 IS - 17 SP - 5260 EP - 5301 PG - 42 SN - 1073-7928 DO - 10.1093/imrn/rnw154 UR - https://m2.mtmt.hu/api/publication/26889890 ID - 26889890 LA - English DB - MTMT ER - TY - JOUR AU - Bidaut-Veron, Marie Francoise TI - LOCAL AND GLOBAL ESTIMATES OF SOLUTIONS OF HAMILTON-JACOBI PARABOLIC EQUATION WITH ABSORPTION JF - ADVANCES IN DIFFERENTIAL EQUATIONS J2 - ADV DIFF EQU VL - 20 PY - 2015 IS - 11-12 SP - 1033 EP - 1066 PG - 34 SN - 1079-9389 UR - https://m2.mtmt.hu/api/publication/25312041 ID - 25312041 LA - English DB - MTMT ER - TY - JOUR AU - Bidaut-Veron, Marie-Francoise AU - Nguyen, Anh Dao TI - Initial Trace of Solutions of Hamilton-Jacobi Parabolic Equation with Absorption JF - ADVANCED NONLINEAR STUDIES J2 - ADV NONLINEAR STUD VL - 15 PY - 2015 IS - 4 SP - 889 EP - 921 PG - 33 SN - 1536-1365 UR - https://m2.mtmt.hu/api/publication/25312042 ID - 25312042 LA - English DB - MTMT ER - TY - JOUR AU - Escudero, Carlos AU - Gazzola, Filippo AU - Feral, Ireneo TI - Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES J2 - J MATH PURE APPL VL - 103 PY - 2015 IS - 4 SP - 924 EP - 957 PG - 34 SN - 0021-7824 DO - 10.1016/j.matpur.2014.09.007 UR - https://m2.mtmt.hu/api/publication/24802299 ID - 24802299 LA - English DB - MTMT ER - TY - JOUR AU - Gladkov, A TI - Self-Similar Blow-Up Solutions of the KPZ Equation JF - INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS J2 - INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS VL - 2015 PY - 2015 SN - 1687-9643 DO - 10.1155/2015/572841 UR - https://m2.mtmt.hu/api/publication/25497103 ID - 25497103 LA - English DB - MTMT ER - TY - JOUR AU - Shang, Haifeng AU - Cheng, Junxiang TI - Cauchy problem for doubly degenerate parabolic equation with gradient source JF - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS J2 - NONLINEAR ANAL-THEOR VL - 113 PY - 2015 SP - 323 EP - 338 PG - 16 SN - 0362-546X DO - 10.1016/j.na.2014.10.006 UR - https://m2.mtmt.hu/api/publication/24802300 ID - 24802300 LA - English DB - MTMT ER - TY - JOUR AU - Shang, Haifeng AU - Sun, Junling AU - Deng, Lihua TI - Cauchy problem for doubly singular parabolic equation with gradient source JF - MATHEMATISCHE NACHRICHTEN J2 - MATH NACHR VL - 288 PY - 2015 IS - 17-18 SP - 2109 EP - 2128 PG - 20 SN - 0025-584X DO - 10.1002/mana.201500010 UR - https://m2.mtmt.hu/api/publication/25774628 ID - 25774628 LA - English DB - MTMT ER - TY - JOUR AU - Cheridito, Patrick AU - Nam, Kihun TI - BSDEs with terminal conditions that have bounded Malliavin derivative JF - JOURNAL OF FUNCTIONAL ANALYSIS J2 - J FUNCT ANAL VL - 266 PY - 2014 IS - 3 SP - 1257 EP - 1285 PG - 29 SN - 0022-1236 DO - 10.1016/j.jfa.2013.12.004 UR - https://m2.mtmt.hu/api/publication/24802303 ID - 24802303 LA - English DB - MTMT ER - TY - JOUR AU - Iagar, Razvan Gabriel AU - Laurencot, Philippe TI - Asymptotic behavior for a singular diffusion equation with gradient absorption JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 256 PY - 2014 IS - 8 SP - 2739 EP - 2777 PG - 39 SN - 0022-0396 DO - 10.1016/j.jde.2014.01.016 UR - https://m2.mtmt.hu/api/publication/24802305 ID - 24802305 LA - English DB - MTMT ER - TY - JOUR AU - Li, Nan AU - Zheng, Pan AU - Mu, Chunlai AU - Ahmed, Iftikhar TI - Large time behavior of solutions for the porous medium equation with a nonlinear gradient source JF - BOUNDARY VALUE PROBLEMS J2 - BOUND VALUE PROBL VL - 2014 PY - 2014 SP - 1 PG - 20 SN - 1687-2762 DO - 10.1186/1687-2770-2014-98 UR - https://m2.mtmt.hu/api/publication/24802301 ID - 24802301 LA - English DB - MTMT ER - TY - JOUR AU - Shang, Haifeng TI - Cauchy problem for nonlinear parabolic equations with a gradient term JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 257 PY - 2014 IS - 8 SP - 2801 EP - 2825 PG - 25 SN - 0022-0396 DO - 10.1016/j.jde.2014.05.049 UR - https://m2.mtmt.hu/api/publication/24802302 ID - 24802302 LA - English DB - MTMT ER - TY - JOUR AU - Zheng, P AU - Mu, C AU - Zhang, F AU - Ahmed, I TI - Waiting time phenomena for the porous medium equation with gradient absorption JF - JOURNAL OF APPLIED MATHEMATICS AND COMPUTING J2 - J APPL MATH COMPUT VL - 47 PY - 2014 IS - 1-2 SP - 225 EP - 236 PG - 12 SN - 1598-5865 DO - 10.1007/s12190-014-0771-8 UR - https://m2.mtmt.hu/api/publication/25497105 ID - 25497105 LA - English DB - MTMT ER - TY - JOUR AU - Abdellaoui, B AU - Nasri, Y AU - Primo, A TI - Strong Regularizing Effect of a Gradient Term in the Heat Equation with a Weight JF - MEDITERRANEAN JOURNAL OF MATHEMATICS J2 - MEDITERR J MATH VL - 10 PY - 2013 IS - 1 SP - 289 EP - 311 PG - 23 SN - 1660-5446 DO - 10.1007/s00009-011-0172-2 UR - https://m2.mtmt.hu/api/publication/23006085 ID - 23006085 LA - English DB - MTMT ER - TY - JOUR AU - Bidaut-Veron, Marie Francoise AU - Nguyen, Anh Dao TI - L-infinity estimates and uniqueness results for nonlinear parabolic equations with gradient absorption terms JF - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS J2 - NONLINEAR ANAL-THEOR VL - 91 PY - 2013 SP - 121 EP - 152 PG - 32 SN - 0362-546X DO - 10.1016/j.na.2013.06.013 UR - https://m2.mtmt.hu/api/publication/24802308 ID - 24802308 LA - English DB - MTMT ER - TY - JOUR AU - Masiero, Federica AU - Richou, Adrien TI - A note on the existence of solutions to Markovian superquadratic BSDEs with an unbounded terminal condition JF - ELECTRONIC JOURNAL OF PROBABILITY J2 - ELECTRON J PROBAB VL - 18 PY - 2013 SP - 1 EP - 15 PG - 15 SN - 1083-6489 DO - 10.1214/EJP.v18-2124 UR - https://m2.mtmt.hu/api/publication/25657617 ID - 25657617 LA - English DB - MTMT ER - TY - JOUR AU - Shang, Haifeng TI - Doubly nonlinear parabolic equations with measure data JF - ANNALI DI MATEMATICA PURA ED APPLICATA J2 - ANN MAT PUR APPL VL - 192 PY - 2013 IS - 2 SP - 273 EP - 296 PG - 24 SN - 0373-3114 DO - 10.1007/s10231-011-0223-0 UR - https://m2.mtmt.hu/api/publication/24802310 ID - 24802310 LA - English DB - MTMT ER - TY - JOUR AU - Shang, Haifeng TI - Global existence and non-existence for the degenerate and uniformly parabolic equations with gradient term JF - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS J2 - P ROY SOC EDINB A VL - 143 PY - 2013 IS - 3 SP - 643 EP - 668 PG - 26 SN - 0308-2105 DO - 10.1017/S030821051100103X UR - https://m2.mtmt.hu/api/publication/24802309 ID - 24802309 LA - English DB - MTMT ER - TY - JOUR AU - Bidaut-Veron, MF AU - Dao, NA TI - ISOLATED INITIAL SINGULARITIES FOR THE VISCOUS HAMILTON-JACOBI EQUATION JF - ADVANCES IN DIFFERENTIAL EQUATIONS J2 - ADV DIFF EQU VL - 17 PY - 2012 IS - 9-10 SP - 903 EP - 934 PG - 32 SN - 1079-9389 UR - https://m2.mtmt.hu/api/publication/23006070 ID - 23006070 LA - English DB - MTMT ER - TY - JOUR AU - Cheridito, P AU - Stadje, M TI - Existence, minimality and approximation of solutions to BSDEs with convex drivers JF - STOCHASTIC PROCESSES AND THEIR APPLICATIONS J2 - STOCH PROC APPL VL - 122 PY - 2012 IS - 4 SP - 1540 EP - 1565 PG - 26 SN - 0304-4149 DO - 10.1016/j.spa.2011.12.008 UR - https://m2.mtmt.hu/api/publication/23006071 ID - 23006071 LA - English DB - MTMT ER - TY - JOUR AU - Gorsky, A AU - Nechaev, S AU - Santachiara, R AU - Schehr, G TI - Random ballistic growth and diffusion in symmetric spaces JF - NUCLEAR PHYSICS B J2 - NUCL PHYS B VL - 862 PY - 2012 IS - 1 SP - 167 EP - 192 PG - 26 SN - 0550-3213 DO - 10.1016/j.nuclphysb.2012.04.005 UR - https://m2.mtmt.hu/api/publication/23006068 ID - 23006068 LA - English DB - MTMT ER - TY - JOUR AU - Iagar, RG AU - Laurencot, P TI - Positivity, decay, and extinction for a singular diffusion equation with gradient absorption JF - JOURNAL OF FUNCTIONAL ANALYSIS J2 - J FUNCT ANAL VL - 262 PY - 2012 IS - 7 SP - 3186 EP - 3239 PG - 54 SN - 0022-1236 DO - 10.1016/j.jfa.2012.01.013 UR - https://m2.mtmt.hu/api/publication/23006069 ID - 23006069 LA - English DB - MTMT ER - TY - JOUR AU - Shang, HF TI - Cauchy problem for fast diffusion equations with a gradient term JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 396 PY - 2012 IS - 1 SP - 133 EP - 144 PG - 12 SN - 0022-247X DO - 10.1016/j.jmaa.2012.06.003 UR - https://m2.mtmt.hu/api/publication/23006072 ID - 23006072 LA - English DB - MTMT ER - TY - JOUR AU - Da, Lio F AU - Ley, O TI - Convex Hamilton-Jacobi equations under superlinear growth conditions on data JF - APPLIED MATHEMATICS AND OPTIMIZATION J2 - APPL MATH OPT VL - 63 PY - 2011 IS - 3 SP - 309 EP - 339 PG - 31 SN - 0095-4616 DO - 10.1007/s00245-010-9122-9 UR - https://m2.mtmt.hu/api/publication/21683623 ID - 21683623 LA - English DB - MTMT ER - TY - JOUR AU - Delbaen, F AU - Hu, Y AU - Bao, X TI - Backward SDEs with superquadratic growth JF - PROBABILITY THEORY AND RELATED FIELDS J2 - PROBAB THEORY REL VL - 150 PY - 2011 IS - 1-2 SP - 145 EP - 192 PG - 48 SN - 0178-8051 DO - 10.1007/s00440-010-0271-1 UR - https://m2.mtmt.hu/api/publication/21683624 ID - 21683624 LA - English DB - MTMT ER - TY - JOUR AU - Namlyeyeva, Y V AU - Taranets, R M TI - Backward motion and waiting time phenomena for degenerate parabolic equations with nonlinear gradient absorption JF - MANUSCRIPTA MATHEMATICA J2 - MANUSCRIPTA MATH VL - 136 PY - 2011 IS - 3 SP - 475 EP - 500 PG - 26 SN - 0025-2611 DO - 10.1007/s00229-011-0454-9 UR - https://m2.mtmt.hu/api/publication/21683625 ID - 21683625 LA - English DB - MTMT ER - TY - JOUR AU - Shang, H TI - On the Cauchy problem for the singular parabolic equations with gradient term JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 378 PY - 2011 IS - 2 SP - 578 EP - 591 PG - 14 SN - 0022-247X DO - 10.1016/j.jmaa.2011.01.024 UR - https://m2.mtmt.hu/api/publication/21683622 ID - 21683622 LA - English DB - MTMT ER - TY - JOUR AU - Abdellaoui, B AU - Peral, I AU - Primo, A TI - Optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a Hardy potential JF - ADVANCES IN MATHEMATICS J2 - ADV MATH VL - 225 PY - 2010 IS - 6 SP - 2967 EP - 3021 PG - 55 SN - 0001-8708 DO - 10.1016/j.aim.2010.04.028 UR - https://m2.mtmt.hu/api/publication/21683626 ID - 21683626 LA - English DB - MTMT ER - TY - JOUR AU - Barles, G AU - Laurençot, P AU - Stinner, C TI - Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton-Jacobi equation JF - ASYMPTOTIC ANALYSIS J2 - ASYMPTOTIC ANAL VL - 67 PY - 2010 IS - 3-4 SP - 229 EP - 250 PG - 22 SN - 0921-7134 DO - 10.3233/ASY-2010-0981 UR - https://m2.mtmt.hu/api/publication/21683629 ID - 21683629 LA - English DB - MTMT ER - TY - JOUR AU - Li, YX AU - Souplet, P TI - Single-Point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equations in Planar Domains JF - COMMUNICATIONS IN MATHEMATICAL PHYSICS J2 - COMMUN MATH PHYS VL - 293 PY - 2010 IS - 2 SP - 499 EP - 517 PG - 19 SN - 0010-3616 DO - 10.1007/s00220-009-0936-8 UR - https://m2.mtmt.hu/api/publication/23006073 ID - 23006073 LA - English DB - MTMT ER - TY - JOUR AU - Stinner, C TI - Convergence to steady states in a viscous Hamilton-Jacobi equation with degenerate diffusion JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 248 PY - 2010 IS - 2 SP - 209 EP - 228 PG - 20 SN - 0022-0396 DO - 10.1016/j.jde.2009.09.019 UR - https://m2.mtmt.hu/api/publication/21683628 ID - 21683628 LA - English DB - MTMT ER - TY - JOUR AU - Tabet, Tchamba T TI - Large time behavior of solutions of viscous hamilton-jacobi equations with superquadratic hamiltonian JF - ASYMPTOTIC ANALYSIS J2 - ASYMPTOTIC ANAL VL - 66 PY - 2010 IS - 3-4 SP - 161 EP - 186 PG - 26 SN - 0921-7134 DO - 10.3233/ASY-2009-0965 UR - https://m2.mtmt.hu/api/publication/21683627 ID - 21683627 LA - English DB - MTMT ER - TY - JOUR AU - Benachour, S AU - Ben-Artzi, M AU - Laurencot, P TI - SHARP DECAY ESTIMATES AND VANISHING VISCOSITY FOR DIFFUSIVE HAMILTON-JACOBI EQUATIONS JF - ADVANCES IN DIFFERENTIAL EQUATIONS J2 - ADV DIFF EQU VL - 14 PY - 2009 IS - 1-2 SP - 1 EP - 25 PG - 25 SN - 1079-9389 UR - https://m2.mtmt.hu/api/publication/23006074 ID - 23006074 LA - English DB - MTMT ER - TY - JOUR AU - Hirata, D TI - A class of semilinear parabolic equations with singular initial data JF - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS J2 - NONLINEAR ANAL-THEOR VL - 70 PY - 2009 IS - 6 SP - 2403 EP - 2415 PG - 13 SN - 0362-546X DO - 10.1016/j.na.2008.03.025 UR - https://m2.mtmt.hu/api/publication/21683631 ID - 21683631 LA - English DB - MTMT ER - TY - JOUR AU - Shang, H AU - Li, F TI - Singular parabolic equations with measures as initial data JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 247 PY - 2009 IS - 6 SP - 1720 EP - 1745 PG - 26 SN - 0022-0396 DO - 10.1016/j.jde.2009.06.003 UR - https://m2.mtmt.hu/api/publication/21683630 ID - 21683630 LA - English DB - MTMT ER - TY - JOUR AU - Abdellaoui, B AU - Dall, Aglio A AU - Peral, I TI - Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES J2 - J MATH PURE APPL VL - 90 PY - 2008 IS - 3 SP - 242 EP - 269 PG - 28 SN - 0021-7824 DO - 10.1016/j.matpur.2008.04.004 UR - https://m2.mtmt.hu/api/publication/21683632 ID - 21683632 LA - English DB - MTMT ER - TY - JOUR AU - Bartier, J -P AU - Laurençot, Ph TI - Gradient estimates for a degenerate parabolic equation with gradient absorption and applications JF - JOURNAL OF FUNCTIONAL ANALYSIS J2 - J FUNCT ANAL VL - 254 PY - 2008 IS - 3 SP - 851 EP - 878 PG - 28 SN - 0022-1236 DO - 10.1016/j.jfa.2007.10.012 UR - https://m2.mtmt.hu/api/publication/21683633 ID - 21683633 LA - English DB - MTMT ER - TY - JOUR AU - Gladkov, A AU - Guedda, M AU - Kersner, Róbert TI - A KPZ growth model with possibly unbounded data: Correctness and blow-up JF - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS J2 - NONLINEAR ANAL-THEOR VL - 68 PY - 2008 IS - 7 SP - 2079 EP - 2091 PG - 13 SN - 0362-546X DO - 10.1016/j.na.2007.01.033 UR - https://m2.mtmt.hu/api/publication/1756292 ID - 1756292 AB - Existence and uniqueness results for initial value problem with a given growth condition (upper bound) on the initial datum for the so-called generalized deterministic KPZ (Kardar-Parisi-Zhang) equation ut = ux x + λ | ux |q are obtained. Self-similar blow-up solutions are investigated also. © 2007 Elsevier Ltd. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Karch, G AU - WoyczyŃski, W A TI - Fractal hamilton-jacobi-kpz equations JF - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - T AM MATH SOC VL - 360 PY - 2008 IS - 5 SP - 2423 EP - 2442 PG - 20 SN - 0002-9947 DO - 10.1090/S0002-9947-07-04389-9 UR - https://m2.mtmt.hu/api/publication/21683635 ID - 21683635 LA - English DB - MTMT ER - TY - JOUR AU - Ma, L AU - Zhao, L AU - Song, X TI - Gradient estimate for the degenerate parabolic equation ut = Δ F (u) + H (u) on manifolds JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 244 PY - 2008 IS - 5 SP - 1157 EP - 1177 PG - 21 SN - 0022-0396 DO - 10.1016/j.jde.2007.08.014 UR - https://m2.mtmt.hu/api/publication/21683634 ID - 21683634 LA - English DB - MTMT ER - TY - JOUR AU - Benachour, S AU - Dbuleanu-Hapca, S AU - Laurenot, P TI - Decay estimates for a viscous Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions JF - ASYMPTOTIC ANALYSIS J2 - ASYMPTOTIC ANAL VL - 51 PY - 2007 IS - 3-4 SP - 209 EP - 229 PG - 21 SN - 0921-7134 UR - https://m2.mtmt.hu/api/publication/21683637 ID - 21683637 LA - English DB - MTMT ER - TY - JOUR AU - Dall'Aglio, A AU - Giachetti, D AU - Segura, de Leon S TI - NONLINEAR PARABOLIC PROBLEMS WITH A VERY GENERAL QUADRATIC GRADIENT TERM JF - DIFFERENTIAL AND INTEGRAL EQUATIONS J2 - DIFFER INTEGR EQUAT VL - 20 PY - 2007 IS - 4 SP - 361 EP - 396 PG - 36 SN - 0893-4983 UR - https://m2.mtmt.hu/api/publication/24802312 ID - 24802312 LA - English DB - MTMT ER - TY - JOUR AU - Fang, Zhong Bo AU - Kwak, Minkyu TI - Complete classification of shape functions of self-similar solutions JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 330 PY - 2007 IS - 2 SP - 1447 EP - 1464 PG - 18 SN - 0022-247X DO - 10.1016/j.jmaa.2006.08.042 UR - https://m2.mtmt.hu/api/publication/25687101 ID - 25687101 LA - English DB - MTMT ER - TY - JOUR AU - Gallay, T AU - Laurencot, P TI - Asymptotic behavior for a viscous Hamilton-Jacobi equation with critical exponent JF - INDIANA UNIVERSITY MATHEMATICS JOURNAL J2 - INDIANA U MATH J VL - 56 PY - 2007 IS - 1 SP - 459 EP - 479 PG - 21 SN - 0022-2518 DO - 10.1512/iumj.2007.56.3107 UR - https://m2.mtmt.hu/api/publication/23006076 ID - 23006076 LA - English DB - MTMT ER - TY - JOUR AU - Laurencot, P TI - Convergence to steady states for a one-dimensional viscous Hamilton-Jacobi equation with Dirichlet boundary conditions JF - PACIFIC JOURNAL OF MATHEMATICS J2 - PAC J MATH VL - 230 PY - 2007 IS - 2 SP - 347 EP - 364 PG - 18 SN - 0030-8730 DO - 10.2140/pjm.2007.230.347 UR - https://m2.mtmt.hu/api/publication/23006075 ID - 23006075 LA - English DB - MTMT ER - TY - JOUR AU - Leonori, T AU - Petitta, F TI - Asymptotic behavior for solutions of parabolic equations with natural growth terms and irregular data JF - ASYMPTOTIC ANALYSIS J2 - ASYMPTOTIC ANAL VL - 48 PY - 2006 IS - 3 SP - 219 EP - 233 PG - 15 SN - 0921-7134 UR - https://m2.mtmt.hu/api/publication/21683641 ID - 21683641 LA - English DB - MTMT ER - TY - JOUR AU - Souplet, P AU - Zhang, QS TI - Global solutions of inhomogeneous Hamilton-Jacobi equations JF - JOURNAL D ANALYSE MATHEMATIQUE J2 - J ANAL MATH VL - 99 PY - 2006 SP - 355 EP - 396 PG - 42 SN - 0021-7670 DO - 10.1007/BF02789452 UR - https://m2.mtmt.hu/api/publication/23006077 ID - 23006077 LA - English DB - MTMT ER - TY - JOUR AU - Souplet, P AU - Zhang, Q S TI - Sharp gradient estimate and Yau's Liouville theorem for the heat equation on noncompact manifolds JF - BULLETIN OF THE LONDON MATHEMATICAL SOCIETY J2 - B LOND MATH SOC VL - 38 PY - 2006 IS - 6 SP - 1045 EP - 1053 PG - 9 SN - 0024-6093 DO - 10.1112/S0024609306018947 UR - https://m2.mtmt.hu/api/publication/21683640 ID - 21683640 LA - English DB - MTMT ER - TY - JOUR AU - Souplet, P AU - Vázquez, J L TI - Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem JF - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES A J2 - DISCRETE CONT DYN S VL - 14 PY - 2006 IS - 1 SP - 221 EP - 234 PG - 14 SN - 1078-0947 DO - 10.3934/dcds.2006.14.221 UR - https://m2.mtmt.hu/api/publication/21683639 ID - 21683639 LA - English DB - MTMT ER - TY - JOUR AU - Benachour, S AU - Dabuleanu, S TI - Large time behavior for a viscous Hamilton-Jacobi equation with Neumann boundary condition JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 216 PY - 2005 IS - 1 SP - 223 EP - 258 PG - 36 SN - 0022-0396 DO - 10.1016/j.jde.2005.02.017 UR - https://m2.mtmt.hu/api/publication/23006081 ID - 23006081 LA - English DB - MTMT ER - TY - JOUR AU - Dabuleanu, S TI - The Cauchy-Neumann problem for a viscous Hamilton-Jacobi equation JF - JOURNAL OF EVOLUTION EQUATIONS J2 - J EVOL EQU VL - 5 PY - 2005 IS - 1 SP - 35 EP - 60 PG - 26 SN - 1424-3199 DO - 10.1007/s00028-004-0154-y UR - https://m2.mtmt.hu/api/publication/23006078 ID - 23006078 LA - English DB - MTMT ER - TY - JOUR AU - Gilding, BH TI - The Cauchy problem for u(t)=Delta u+vertical bar del u vertical bar(q), large-time behaviour JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES J2 - J MATH PURE APPL VL - 84 PY - 2005 IS - 6 SP - 753 EP - 785 PG - 33 SN - 0021-7824 DO - 10.1016/j.matpur.2004.11.003 UR - https://m2.mtmt.hu/api/publication/23006079 ID - 23006079 LA - English DB - MTMT ER - TY - JOUR AU - Laurencot, P AU - Souplet, P TI - Optimal growth rates for a viscous Hamilton-Jacobi equation JF - JOURNAL OF EVOLUTION EQUATIONS J2 - J EVOL EQU VL - 5 PY - 2005 IS - 1 SP - 123 EP - 135 PG - 13 SN - 1424-3199 DO - 10.1007/s00028-004-0181-8 UR - https://m2.mtmt.hu/api/publication/23006080 ID - 23006080 LA - English DB - MTMT ER - TY - JOUR AU - Benachour, S AU - Karch, G AU - Laurencot, P TI - Asymptotic profiles of solutions to convection-diffusion equations JF - COMPTES RENDUS MATHEMATIQUE J2 - CR MATH VL - 338 PY - 2004 IS - 5 SP - 369 EP - 374 PG - 6 SN - 1631-073X DO - 10.1016/j.crma.2004.01.001 UR - https://m2.mtmt.hu/api/publication/23006084 ID - 23006084 LA - French DB - MTMT ER - TY - JOUR AU - Benachour, S AU - Karch, G AU - Laurencot, P TI - Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES J2 - J MATH PURE APPL VL - 83 PY - 2004 IS - 10 SP - 1275 EP - 1308 PG - 34 SN - 0021-7824 DO - 10.1016/j.matpur.2004.03.002 UR - https://m2.mtmt.hu/api/publication/23006083 ID - 23006083 LA - English DB - MTMT ER - TY - JOUR AU - Hesaaraki, M AU - Moameni, A TI - Blow-up of positive solutions for a family of nonlinear parabolic equations in general domain in R-N JF - MICHIGAN MATHEMATICAL JOURNAL J2 - MICH MATH J VL - 52 PY - 2004 IS - 2 SP - 375 EP - 389 PG - 15 SN - 0026-2285 DO - 10.1307/mmj/1091112081 UR - https://m2.mtmt.hu/api/publication/23006082 ID - 23006082 LA - English DB - MTMT ER -