Archive for Rational Mechanics and Analysis

, Volume 194, Issue 3, pp 887–925 | Cite as

Two-phase Entropy Solutions of a Forward–Backward Parabolic Equation

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Abstract

This article deals with the Cauchy problem for a forward–backward parabolic equation, which is of interest in physical and biological models. Considering such an equation as the singular limit of an appropriate pseudoparabolic third-order regularization, we consider the framework of entropy solutions, namely weak solutions satisfying an additional entropy inequality inherited by the higher order equation. Moreover, we restrict the attention to two-phase solutions, that is solutions taking values in the intervals where the parabolic equation iswell-posed, proving existence and uniqueness of such solutions.

Keywords

Entropy Weak Solution Cauchy Problem Parabolic Equation Boundary Problem 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Corrado Mascia
    • 1
  • Andrea Terracina
    • 1
  • Alberto Tesei
    • 1
  1. 1.Dipartimento di Matematica “G. Castelnuovo”Università di Roma “La Sapienza”RomeItaly

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