Research article

A class of thermal sub-differential contact problems

  • 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

    Related Papers:

  • 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.


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    [7] P. D. Panagiotopoulos, Hemivariational Inequalities, applications in Mechanics and Engineering, Contributions to Nonlinear Functional Analysis, Springer-Verlag, 1993.
    [8] N. Costea, V. Radulescu, Hartman-Stampacchia results for stably pseudomonotone operators and non-linear hemivariational inequalities, Appl. Anal., 89 (2010): 175-88.
    [9] E. Zeidler, Nonlinear Functional Analysis and its Applications, Contributions to Nonlinear Functional Analysis, Springer Verlag, 1997.
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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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