Solvability of a class of thermal dynamical contact problems  with subdifferential conditions

Samir Adly; Oanh Chau; Mohamed Rochdi

doi:10.3934/naco.2012.2.91

Article Contents

2012, Volume 2, Issue 1: 91-104. Doi: 10.3934/naco.2012.2.91

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Solvability of a class of thermal dynamical contact problems with subdifferential conditions

1.
Institut d'Ingénierie Informatique de Limoges and LACO, URA-1586, 123 Avenue A. Thomas, 87060 Limoges Cedex
2.
Université de La Réunion, Département Maths-Info, BP 7151, 15 Avenue René Cassin, 97715 Saint Denis Messag, cedex 09, La Réunion

Received: December 31, 2010

Revised: July 31, 2011

Published: February 2012

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Abstract

We study a class of dynamic thermal sub-differential contact problems with friction, for long memory visco-elastic materials, which can be put into a general model of system defined by a second order evolution inequality, coupled with a first order evolution equation. We present and establish an existence and uniqueness result, by using general results on first order evolution inequality, with monotone operators and fixed point methods.

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Mathematics Subject Classification: Primary: 74M10, 74M15, 74F25, 74H20, 74H25, 34G20.

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