AIMS Mathematics, 2017, 2(4): 658-681. doi: 10.3934/Math.2017.4.658

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A class of thermal sub-differential contact problems

Université de La Réunion, Département de Mathématiques, BP 7151, 15 Avenue René Cassin, 97715 Saint Denis Messag, cedex 09, La Réunion, France

We study a class of dynamic sub-differential contact problems with friction, and thermale ects, for time depending long memory visco-elastic materials, with or without the clamped condition.We describe the mechanical problem, derive its variational formulation, and after specifyingthe assumptions on the data and operators, we prove an existence and uniqueness of weak solutionon displacement and temperature fields. Then we present a fully discrete scheme for numerical approximationsof the different solutions, and provide analysis of error order estimates. Finally variousnumerical computations in dimension two will be given.
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