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Title: Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent

The paper is concerned with the solvability of the initial-boundary value problem for second-order parabolic equations with variable nonlinearity exponents. In the model case, this equation contains the p-Laplacian with a variable exponent p(x,t). The problem is shown to be uniquely solvable, provided the exponent p is bounded away from both 1 and ∞ and is log-Hölder continuous, and its solution satisfies the energy equality. Bibliography: 18 titles.
Authors:
;  [1]
  1. A.G. and N.G.Stoletov Vladimir State University, Vladimir (Russian Federation)
Publication Date:
OSTI Identifier:
22365576
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 3; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY-VALUE PROBLEMS; LAPLACIAN; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTIZATION