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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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On the Property of Finite Speed of the Perturbation Propagation for the Solution of Dirichlet's Problem for Nonlinear Inhomogeneous Diffusion Equation

Author(s):

Alexander Fedorovich Tedeev

PhD in phisics and mathematics
Assoc.Professor
Dept. of functional analysis and differential equations
K. Khetagurov North-Osetian State University
Vatutin str. 44-46,
362025, Vladikaukaz, RSO-A, Russia

tedeev92@bk.ru

Abstract:

The paper deals with the Cauchy-Dirichlet problem for the nonlinear inhomogeneous diffusion equation with the possible power degeneration conditions near the boundary of a cone-like domain. Our main technical tool for the obtaining of solution estimations is a suitable weighted Nerenberg-Gagliardo type inequality, which in turn is connected to a weighted isoperimetric inequality characterizing the geometry of the domain. On this basis we study the property of finite speed of the perturbation propagation of the solution. The suffucient conditions ensuring the possibility to estimate the radius of a solution support in the absence of a source are given. The existence of a strong generalized solution has been proved.

Keywords

References:

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