TY - JOUR AU - Barna, Imre Ferenc AU - Vadászné Bognár, Gabriella AU - Guedda, M. AU - Mátyás, L. AU - Hriczó, Krisztián TI - Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise terms JF - MATHEMATICAL MODELLING AND ANALYSIS J2 - MATH MODEL ANAL VL - 25 PY - 2020 IS - 2 SP - 241 EP - 256 PG - 16 SN - 1392-6292 DO - 10.3846/mma.2020.10459 UR - https://m2.mtmt.hu/api/publication/31272217 ID - 31272217 LA - English DB - MTMT ER - TY - JOUR AU - Muravnik, A. B. TI - Decay of Nonnegative Solutions of Singular Parabolic Equations with KPZ-Nonlinearities JF - COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS J2 - COMPUT MATH MATH PHYS VL - 60 PY - 2020 IS - 8 SP - 1375 EP - 1380 PG - 6 SN - 0965-5425 DO - 10.1134/S0965542520080126 UR - https://m2.mtmt.hu/api/publication/31688464 ID - 31688464 AB - The Cauchy problem for quasilinear parabolic equations with KPZ-nonlinearities is considered. It is proved that the behavior of the solution as -> infinity documentclass can change substantially as compared with the homogeneous case if the equation involves zero-order terms. More specifically, the solution decays at infinity irrespective of the behavior of the initial function and the rate and character of this decay depend on the conditions imposed on the lower order coefficients of the equation. LA - English DB - MTMT ER - TY - JOUR AU - Muravnik, A. B. TI - Nonclassical stationary and nonstationary problems with weight Neumann conditions for singular equations with KPZ-nonlinearities JF - COMPLEX VARIABLES AND ELLIPTIC EQUATIONS J2 - COMPLEX VAR ELLIPTIC PY - 2020 PG - 8 SN - 1747-6933 DO - 10.1080/17476933.2020.1783662 UR - https://m2.mtmt.hu/api/publication/31688462 ID - 31688462 AB - From a unique viewpoint, singular elliptic and parabolic second-order inequalities with quasilinear KPZ-type terms are investigated in cylindrical domains. The weight Neumann condition is set on the lateral area of the cylinder; no condition is set on the base of the cylinder (regardless the type of the equation). Results of two kinds are established: the existence of a limit of each solution (if it exists) along the axis of the cylinder and sufficient conditions of a blow-up (including instant or complete one). LA - English DB - MTMT ER - TY - JOUR AU - Muravnik, A. B. TI - On absence of global solutions of quasilinear differential-convolutional inequalities JF - COMPLEX VARIABLES AND ELLIPTIC EQUATIONS J2 - COMPLEX VAR ELLIPTIC VL - 65 PY - 2020 IS - 6 SP - 977 EP - 985 PG - 9 SN - 1747-6933 DO - 10.1080/17476933.2019.1639049 UR - https://m2.mtmt.hu/api/publication/30901955 ID - 30901955 AB - From a unique viewpoint, elliptic and parabolic second-order inequalities with quasilinear KPZ-type terms and nonlocal convolutional terms arising in the description of reaction-diffusion processes, neural networks, and nonlocal phase transitions are investigated. Sufficient conditions of the absence of their global solutions, i.e. necessary conditions of their global solvability, are found. LA - English DB - MTMT ER - TY - JOUR AU - Muravnik, A. B. TI - On absence of global positive solutions of elliptic inequalities with KPZ-nonlinearities JF - COMPLEX VARIABLES AND ELLIPTIC EQUATIONS J2 - COMPLEX VAR ELLIPTIC VL - 64 PY - 2019 IS - 5 SP - 736 EP - 740 PG - 5 SN - 1747-6933 DO - 10.1080/17476933.2018.1501037 UR - https://m2.mtmt.hu/api/publication/30901956 ID - 30901956 AB - For quasilinear elliptic partial differential inequalities containing nonlinearities of the KPZ type, arising in various applications, we find sufficient conditions of the absence of global positive solutions, i.e. necessary conditions of the existence of global positive solutions. LA - English DB - MTMT ER - TY - JOUR AU - Muravnik, A. B. TI - ON QUALITATIVE PROPERTIES OF SOLUTIONS TO QUASILINEAR PARABOLIC EQUATIONS ADMITTING DEGENERATIONS AT INFINITY JF - Ufa Mathematical Journal J2 - Ufa Mathematical Journal VL - 10 PY - 2018 IS - 4 SP - 77 EP - 84 PG - 8 SN - 2304-0122 DO - 10.13108/2018-10-4-77 UR - https://m2.mtmt.hu/api/publication/30462860 ID - 30462860 AB - We consider the Cauchy problem for a quasilinear parabolic equations rho(x)u(t) =Delta u+ g(u)vertical bar Delta u vertical bar(2), where the positive coefficient rho degenerates at infinity, while the coefficient g either is a continuous function or have singularities of at most first power. These nonlinearities called Kardar-Parisi-Zhang nonlinearities (or KPZ-nonlinearities) arise in various applications (in particular, in modelling directed polymer and interface growth). Also, they are of an independent theoretical interest because they contain the second powers of the first derivatives: this is the greatest exponent such that Bernstein-type conditions for the corresponding elliptic problem ensure apriori L-infinity-estimates of first order derivatives of the solution via the L-infinity-estimate of the solution itself. Earlier, the asymptotic properties of solutions to parabolic equations with nonlinearities of the specified kind were studied only for the case of uniformly parabolic linear parts. Once the coefficient rho degenerates (at least at infinity), the nature of the problem changes qualitatively, which is confirmed by the presented study of qualitative properties of (classical) solutions to the specified Cauchy problem. We find conditions for the coefficient rho and the initial function guaranteeing the following behavior of the specified solutions: there exists a (limit) Lipschitz function A(t) such that, for any positive t, the generalized spherical mean of the solution tends to the specified Lipschitz function as the radius of the sphere tends to infinity. The generalized spherical mean is constructed as follows. First, we apply a monotone function to a solution; this monotone function is determined only by the coefficient at the nonlinearity (both in regular and singular cases). Then we compute the mean over the (n - 1)-dimensional sphere centered at the origin (in the linear case, this mean naturally is reduced to a classical spherical mean). To construct the specified monotone function, we use the Bitsadze method allowing us to express solutions of the studied quasilinear equations via solutions of semi-linear equations. LA - English DB - MTMT ER - TY - JOUR AU - Guedda, Mohammed TI - Multiple positive solutions to a singular boundary value problem for a superlinear Emden-Fowler equation JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 352 PY - 2009 IS - 1 SP - 259 EP - 270 PG - 12 SN - 0022-247X DO - 10.1016/j.jmaa.2008.05.028 UR - https://m2.mtmt.hu/api/publication/25687099 ID - 25687099 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 - 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 - Margallo-Balbas, Eduardo AU - Pandraud, Gregory AU - French, Patrick J ED - Dong, L ED - Katagiri, Y ED - Higurashi, E ED - Toshiyoshi, H ED - Peter, YA TI - Thermo-optical delay line for Optical Coherence Tomography JF - PROCEEDINGS OF SPIE - THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING J2 - PROCEEDINGS OF SPIE VL - 6717 PY - 2007 IS - Lausanne PG - 9 SN - 0277-786X DO - 10.1117/12.754324 UR - https://m2.mtmt.hu/api/publication/25687102 ID - 25687102 LA - English DB - MTMT ER -