Singular limit of  an integrodifferential systemrelated to the entropy balance

Elena Bonetti; Pierluigi Colli; Gianni Gilardi

doi:10.3934/dcdsb.2014.19.1935

Article Contents

2014, Volume 19, Issue 7: 1935-1953. Doi: 10.3934/dcdsb.2014.19.1935

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Singular limit of an integrodifferential system related to the entropy balance

1.
Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia

Received: December 31, 2012

Revised: April 30, 2013

Published: August 2014

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Abstract

A thermodynamic model describing phase transitions with thermal memory, in terms of an entropy equation and a momentum balance for the microforces, is adressed. Convergence results and error estimates are proved for the related integrodifferential system of PDE as the sequence of memory kernels converges to a multiple of a Dirac delta, in a suitable sense.

Keywords:

Entropy equation,
thermal memory,
phase field model,
nonlinear partial differential equations,
asymptotics on the memory term.

Mathematics Subject Classification: Primary: 35K55, 35B40; Secondary: 35Q79, 80A22.

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