@article{MTMT:31272217,
	title = {Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise terms},
	url = {https://m2.mtmt.hu/api/publication/31272217},
	author = {Barna, Imre Ferenc and Vadászné Bognár, Gabriella and Guedda, M. and Mátyás, L. and Hriczó, Krisztián},
	doi = {10.3846/mma.2020.10459},
	journal-iso = {MATH MODEL ANAL},
	journal = {MATHEMATICAL MODELLING AND ANALYSIS},
	volume = {25},
	unique-id = {31272217},
	issn = {1392-6292},
	year = {2020},
	eissn = {1648-3510},
	pages = {241-256},
	orcid-numbers = {Barna, Imre Ferenc/0000-0001-6206-3910; Vadászné Bognár, Gabriella/0000-0002-4070-1376; Hriczó, Krisztián/0000-0003-3298-6495}
}

@article{MTMT:31688464,
	title = {Decay of Nonnegative Solutions of Singular Parabolic Equations with KPZ-Nonlinearities},
	url = {https://m2.mtmt.hu/api/publication/31688464},
	author = {Muravnik, A. B.},
	doi = {10.1134/S0965542520080126},
	journal-iso = {COMPUT MATH MATH PHYS},
	journal = {COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS},
	volume = {60},
	unique-id = {31688464},
	issn = {0965-5425},
	abstract = {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.},
	keywords = {Parabolic equations; KPZ-nonlinearities; Quasilinear equations; lower-order terms; behavior at infinity},
	year = {2020},
	eissn = {1555-6662},
	pages = {1375-1380}
}

@article{MTMT:31688462,
	title = {Nonclassical stationary and nonstationary problems with weight Neumann conditions for singular equations with KPZ-nonlinearities},
	url = {https://m2.mtmt.hu/api/publication/31688462},
	author = {Muravnik, A. B.},
	doi = {10.1080/17476933.2020.1783662},
	journal-iso = {COMPLEX VAR ELLIPTIC},
	journal = {COMPLEX VARIABLES AND ELLIPTIC EQUATIONS},
	unique-id = {31688462},
	issn = {1747-6933},
	abstract = {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).},
	keywords = {V; Blow-up; Volpert; global solutions; Quasilinear equations; KPZ-terms; Neumann conditions},
	year = {2020},
	eissn = {1747-6941}
}

@article{MTMT:30901955,
	title = {On absence of global solutions of quasilinear differential-convolutional inequalities},
	url = {https://m2.mtmt.hu/api/publication/30901955},
	author = {Muravnik, A. B.},
	doi = {10.1080/17476933.2019.1639049},
	journal-iso = {COMPLEX VAR ELLIPTIC},
	journal = {COMPLEX VARIABLES AND ELLIPTIC EQUATIONS},
	volume = {65},
	unique-id = {30901955},
	issn = {1747-6933},
	abstract = {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.},
	keywords = {V; Volpert; Quasilinear inequalities; convolutional terms; nonlocal terms; global solutions; nonexistence},
	year = {2020},
	eissn = {1747-6941},
	pages = {977-985}
}

@article{MTMT:30901956,
	title = {On absence of global positive solutions of elliptic inequalities with KPZ-nonlinearities},
	url = {https://m2.mtmt.hu/api/publication/30901956},
	author = {Muravnik, A. B.},
	doi = {10.1080/17476933.2018.1501037},
	journal-iso = {COMPLEX VAR ELLIPTIC},
	journal = {COMPLEX VARIABLES AND ELLIPTIC EQUATIONS},
	volume = {64},
	unique-id = {30901956},
	issn = {1747-6933},
	abstract = {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.},
	keywords = {KPZ-nonlinearities; Quasilinear inequalities; global solutions; nonexistence},
	year = {2019},
	eissn = {1747-6941},
	pages = {736-740}
}

@article{MTMT:30462860,
	title = {ON QUALITATIVE PROPERTIES OF SOLUTIONS TO QUASILINEAR PARABOLIC EQUATIONS ADMITTING DEGENERATIONS AT INFINITY},
	url = {https://m2.mtmt.hu/api/publication/30462860},
	author = {Muravnik, A. B.},
	doi = {10.13108/2018-10-4-77},
	journal-iso = {Ufa Mathematical Journal},
	journal = {Ufa Mathematical Journal},
	volume = {10},
	unique-id = {30462860},
	issn = {2304-0122},
	abstract = {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.},
	keywords = {Parabolic equations; LONG-TIME BEHAVIOR; KPZ-nonlinearities; degeneration at infinity},
	year = {2018},
	pages = {77-84}
}

@article{MTMT:25687099,
	title = {Multiple positive solutions to a singular boundary value problem for a superlinear Emden-Fowler equation},
	url = {https://m2.mtmt.hu/api/publication/25687099},
	author = {Guedda, Mohammed},
	doi = {10.1016/j.jmaa.2008.05.028},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {352},
	unique-id = {25687099},
	issn = {0022-247X},
	year = {2009},
	eissn = {1096-0813},
	pages = {259-270}
}

@article{MTMT:1756292,
	title = {A KPZ growth model with possibly unbounded data: Correctness and blow-up},
	url = {https://m2.mtmt.hu/api/publication/1756292},
	author = {Gladkov, A and Guedda, M and Kersner, Róbert},
	doi = {10.1016/j.na.2007.01.033},
	journal-iso = {NONLINEAR ANAL-THEOR},
	journal = {NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS},
	volume = {68},
	unique-id = {1756292},
	issn = {0362-546X},
	abstract = {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.},
	keywords = {Mathematical models; Initial value problems; Unbounded data; Growth conditions; Jacobian matrices; Viscous Hamilton-Jacobi equation; Surface growth; Self-similar blow-up solutions; KPZ equation},
	year = {2008},
	eissn = {1873-5215},
	pages = {2079-2091}
}

@article{MTMT:25687101,
	title = {Complete classification of shape functions of self-similar solutions},
	url = {https://m2.mtmt.hu/api/publication/25687101},
	author = {Fang, Zhong Bo and Kwak, Minkyu},
	doi = {10.1016/j.jmaa.2006.08.042},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {330},
	unique-id = {25687101},
	issn = {0022-247X},
	year = {2007},
	eissn = {1096-0813},
	pages = {1447-1464}
}

@article{MTMT:25687102,
	title = {Thermo-optical delay line for Optical Coherence Tomography},
	url = {https://m2.mtmt.hu/api/publication/25687102},
	author = {Margallo-Balbas, Eduardo and Pandraud, Gregory and French, Patrick J},
	doi = {10.1117/12.754324},
	editor = {Dong, L and Katagiri, Y and Higurashi, E and Toshiyoshi, H and Peter, YA},
	journal-iso = {PROCEEDINGS OF SPIE},
	journal = {PROCEEDINGS OF SPIE - THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING},
	volume = {6717},
	unique-id = {25687102},
	issn = {0277-786X},
	year = {2007},
	eissn = {1996-756X}
}