Singular Perturbations of Forward-Backward p-Parabolic Equations

Abstract

In this paper we have proved the existence of entropy measure-valued solutions to forward-backward p-parabolic equations. We have obtained these solutions as singular limits of weak solutions to (p,q)-elliptic regularized boundary-value problems as ε → 0+. When q > 1 and q = 2 we have not defined yet admissible initial and final conditions even in the form of integral inequalities.

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Correspondence to S. N. Antontsev.

Additional information

Research supported by project III.22.4.2 Boundary value problem in dynamics of heterogeneous media.

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Antontsev, S.N., Kuznetsov, I.V. Singular Perturbations of Forward-Backward p-Parabolic Equations. J Elliptic Parabol Equ 2, 357–370 (2016). https://doi.org/10.1007/BF03377409

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2010 Mathematics Subject Classification

  • Primary: 35D99, 35K55, 35K65, 35K92
  • Secondary: 28A33, 35B50, 35R25

Key words and phrases

  • entropy solution
  • forward-backward parabolic equation
  • gradient Young measure
  • maximum principle