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 Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 8, Pages 1422–1427 (Mi zvmmf11121)

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

Abstract: The Cauchy problem for quasilinear parabolic equations with KPZ-nonlinearities is considered. It is proved that the behavior of the solution as $t\to\infty$ 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).

DOI: https://doi.org/10.31857/S0044466920080128

English version:
Computational Mathematics and Mathematical Physics, 2020, 60:8, 1375–1380

Bibliographic databases:

UDC: 517.956
Revised: 15.02.2020
Accepted:09.04.2020

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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