A class of thermal sub-differential contact problems

Oanh Chau; Oanh Chau

doi:10.3934/Math.2017.4.658

AIMS Mathematics

2017, Volume 2, Issue 4: 658-681. doi: 10.3934/Math.2017.4.658

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Research article

A class of thermal sub-differential contact problems

Oanh Chau ^,

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

Received: 16 April 2017 Accepted: 28 November 2017 Published: 04 December 2017

We study a class of dynamic sub-differential contact problems with friction, and thermal e 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 specifying the assumptions on the data and operators, we prove an existence and uniqueness of weak solution on displacement and temperature fields. Then we present a fully discrete scheme for numerical approximations of the different solutions, and provide analysis of error order estimates. Finally various numerical computations in dimension two will be given.
Citation: Oanh Chau. A class of thermal sub-differential contact problems[J]. AIMS Mathematics, 2017, 2(4): 658-681. doi: 10.3934/Math.2017.4.658

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Abstract

We study a class of dynamic sub-differential contact problems with friction, and thermal e 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 specifying the assumptions on the data and operators, we prove an existence and uniqueness of weak solution on displacement and temperature fields. Then we present a fully discrete scheme for numerical approximations of the different solutions, and provide analysis of error order estimates. Finally various numerical computations in dimension two will be given.

References

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