A well-posedness result for irreversible phase transitions with a nonlinear heat flux law

Giovanna Bonfanti; Fabio Luterotti

doi:10.3934/dcdss.2013.6.331

Article Contents

2013, Volume 6, Issue 2: 331-351. Doi: 10.3934/dcdss.2013.6.331

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A well-posedness result for irreversible phase transitions with a nonlinear heat flux law

Giovanna Bonfanti^1, and
Fabio Luterotti^1,

1.
Dipartimento di Matematica, Università di Brescia, via Branze 38, 25123 Brescia

Received: September 30, 2011

Revised: February 29, 2012

Published: March 2013

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Abstract

In this paper, we deal with a PDE system describing a phase transition problem characterized by irreversible evolution and ruled by a nonlinear heat flux law. Its derivation comes from the modelling approach proposed by M. Frémond. Our main result consists in showing the global-in-time existence and the uniqueness of the solution of the related initial and boundary value problem.

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Mathematics Subject Classification: Primary: 80A22, 35K55, 35B45.

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