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Singular Perturbations of Forward-Backward p-Parabolic Equations

  • S. N. Antontsev
  • I. V. Kuznetsov
Original Paper

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.

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 

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Copyright information

© Orthogonal Publishing and Springer International Publishing 2016

Authors and Affiliations

  1. 1.Lavrentyev Institute of Hydrodynamics Siberian Branch of RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia
  3. 3.CMAF-CIOUniversity of LisbonLisbonPortugal

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