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On some dynamic thermal non clamped contact problems

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Abstract

We study a class of dynamic thermal sub-differential contact problems with friction, for long memory visco-elastic materials, without the clamped condition, 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. Finally a fully discrete scheme for numerical approximations is provided, and corresponding various numerical computations in dimension two will be given.

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Acknowledgments

The authors would like to thanks the anonymous referees for many helpful comments and valuable suggestions.

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Authors and Affiliations

  1. Laboratoire XLIM, Université de Limoges, 87060 , Limoges Cedex, France

    Samir Adly

  2. Université de La Réunion, 97715 , Saint-Denis Messag cedex 9, La Réunion, France

    Oanh Chau

Authors
  1. Samir Adly
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  2. Oanh Chau
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Correspondence to Samir Adly.

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Dedicated to Jon Borwein in honor of his 60th birthday.

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Adly, S., Chau, O. On some dynamic thermal non clamped contact problems. Math. Program. 139, 5–26 (2013). https://doi.org/10.1007/s10107-013-0657-9

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  • DOI: https://doi.org/10.1007/s10107-013-0657-9

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