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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 8, Pages 1422–1427
DOI: https://doi.org/10.31857/S0044466920080128 (Mi zvmmf11121) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Decay of nonnegative solutions of singular parabolic equations with KPZ-nonlinearities

A. B. Muravnikab

a Joint Stock Company "Concern "Sozvesdie"
b RUDN University, Moscow, 117198 Russia
Citations (5)
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DOI: https://doi.org/10.31857/S0044466920080128
Abstract: The Cauchy problem for quasilinear parabolic equations with KPZ-nonlinearities is considered. It is proved that the behavior of the solution as t→∞ 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.
Key words: parabolic equations, quasilinear equations, KPZ-nonlinearities, lower-order terms, behavior at infinity.
Funding agency
This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00288 A) (Theorems 1, 2) and by the RUDN program “5-100” (Theorems 3, 4).
Received: 15.02.2020
Revised: 15.02.2020
Accepted: 09.04.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 8, Pages 1375–1380
DOI: https://doi.org/10.1134/S0965542520080126
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: A. B. Muravnik, “Decay of nonnegative solutions of singular parabolic equations with KPZ-nonlinearities”, Zh. Vychisl. Mat. Mat. Fiz., 60:8 (2020), 1422–1427; Comput. Math. Math. Phys., 60:8 (2020), 1375–1380
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf11121
  • https://www.mathnet.ru/eng/zvmmf/v60/i8/p1422
    • This publication is cited in the following 5 articles:
    1. N. N. Nefedov, A. O. Orlov, “Existence and stability of stationary solutions with boundary layers in a system of fast and slow reaction–diffusion–advection equations with KPZ nonlinearities”, Theoret. and Math. Phys., 220:1 (2024), 1178–1192  mathnet  crossref  crossref  mathscinet  adsnasa
    2. E.I. Nikulin, N.N. Nefedov, A.O. Orlov, “Existence and Asymptotic Stability of Solutions for Periodic Parabolic Problems in Tikhonov-Type Reaction–Diffusion–Advection Systems with KPZ Nonlinearities”, Russ. J. Math. Phys., 31:3 (2024), 504  crossref
    3. N. N Nefedov, A. O Orlov, “Existence and Stability of Solutions with Internal Transition Layer for the Reaction–Diffusion–Advection Equation with a KPZ-Nonlinearity”, Differentsialnye uravneniya, 59:8 (2023), 1007  crossref
    4. N. N. Nefedov, A. O. Orlov, “Existence and Stability of Solutions with Internal Transition Layer for the Reaction–Diffusion–Advection Equation with a KPZ-Nonlinearity”, Diff Equat, 59:8 (2023), 1009  crossref
    5. Andrey B. Muravnik, “Qualitative Properties of Solutions of Equations and Inequalities with KPZ-Type Nonlinearities”, Mathematics, 11:4 (2023), 990  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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