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Mediterranean Journal of Mathematics

, Volume 11, Issue 4, pp 1129–1148 | Cite as

Existence of Strong Solutions for a Fully Hyperbolic Phase-Field Model Based on Type III Heat Conduction with a Logarithmic Nonlinear Term

  • Alain Miranville
Article
  • 81 Downloads

Abstract

In this paper, we prove the existence (and also the uniqueness) of strong solutions for a fully hyperbolic phase-field model based on type III heat conduction. The model consists of the hyperbolic relaxation of the usual equation for the temperature, coupled with the equation for the thermal displacement variable. We also study the limit problem, as the relaxation parameter goes to 0.

Mathematics Subject Classification (2000)

35K55 35L15 

Keywords

Fully hyperbolic phase-field model type III heat conduction well-posedness 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Applications, UMR CNRS 7348-SP2MIUniversité de PoitiersChasseneuil Futuroscope CedexFrance

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