Existence of entropy measure-valued solutions for forward-backward p-parabolic equations

Stanislav N. Antontsev, Ivan V. Kuznetsov

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper we have proved that the Dirichlet problem for the forward-backward p-parabolic equation has an entropy measurevalued solution which has been obtained as a singular limit of weak solutions and their gradients to the Dirichlet problem for the elliptic equation containing the anisotropic (p, 2)-Laplace operator. In order to guarantee the existence of entropy measure-valued solutions, the initial and final conditions should be formulated in the form of integral inequalities. This means that an entropy measure-valued solution can deviate from both initial and final data on the boundary. Moreover, a gradient Young measure appears in the representation of an entropy measurevalued solution. The uniqueness of entropy measure-valued solutions is still an open question.

Original languageEnglish
Pages (from-to)774-793
Number of pages20
JournalСибирские электронные математические известия
Volume14
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Anisotropic Laplace operator
  • Entropy measure-valued solution
  • Forward-backward parabolic equation
  • Gradient Young measure

OECD FOS+WOS

  • 1.01 MATHEMATICS

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