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Title: Solutions to higher-order anisotropic parabolic equations in unbounded domains

The paper is devoted to a certain class of doubly nonlinear higher-order anisotropic parabolic equations. Using Galerkin approximations it is proved that the first mixed problem with homogeneous Dirichlet boundary condition has a strong solution in the cylinder D=(0,∞)×Ω, where Ω⊂R{sup n}, n≥3, is an unbounded domain. When the initial function has compact support the highest possible rate of decay of this solution as t→∞ is found. An upper estimate characterizing the decay of the solution is established, which is close to the lower estimate if the domain is sufficiently 'narrow'. The same authors have previously obtained results of this type for second order anisotropic parabolic equations. Bibliography: 29 titles.
Authors:
;  [1]
  1. Sterlitamak branch of Bashkir State University, (Russian Federation)
Publication Date:
OSTI Identifier:
22365790
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ANISOTROPY; APPROXIMATIONS; BOUNDARY CONDITIONS; DIRICHLET PROBLEM; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS