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Title: Stabilization of the solution of a doubly nonlinear parabolic equation

The method of Galerkin approximations is employed to prove the existence of a strong global (in time) solution of a doubly nonlinear parabolic equation in an unbounded domain. The second integral identity is established for Galerkin approximations, and passing to the limit in it an estimate for the decay rate of the norm of the solution from below is obtained. The estimates characterizing the decay rate of the solution as x→∞ obtained here are used to derive an upper bound for the decay rate of the solution with respect to time; the resulting estimate is pretty close to the lower one. Bibliography: 17 titles.
Authors:
 [1] ;  [2]
  1. Ufa State Aviation Technical University, Ufa (Russian Federation)
  2. Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa (Russian Federation)
Publication Date:
OSTI Identifier:
22365966
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 9; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; GALERKIN-PETROV METHOD; INTEGRALS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; STABILIZATION