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Differential Equations

, Volume 46, Issue 2, pp 239–254 | Cite as

On the decay of a solution of a nonuniformly parabolic equation

  • V. F. Gilimshina
Partial Differential Equations
  • 38 Downloads

Abstract

For a uniformly parabolic second-order equation with lower-order terms in an unbounded domain, we obtain an upper bound for the decay rate of the solution of the mixed problem with alternating boundary conditions of the first and third types. We prove that the bound is sharp in the case of an equation without lower-order terms in a wide class of domains of revolution. In addition, we show that a solution of a nonuniformly parabolic equation can decay much more rapidly than a solution of a uniformly parabolic equation.

Keywords

Decay Rate Parabolic Equation Unbounded Domain Mixed Problem Harnack Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • V. F. Gilimshina
    • 1
  1. 1.Bashkir State Pedagogical UniversityUfaRussia

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