ITM Web Conf.
Volume 34, 2020International Conference on Applied Mathematics and Numerical Methods – third edition (ICAMNM 2020)
|Number of page(s)||19|
|Published online||03 December 2020|
Tykhonov triples and convergence results for history-dependent variational inequalities
Laboratoire de Mathématiques et Physique University of Perpignan Via Domitia 52 Avenue Paul Alduy, 66860 Perpignan, France
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We deal with the Tykhonov well-posedness of a time-dependent variational inequality deﬁned on the unbounded interval of time ℝ+ = [0, +∞ ), governed by a history-dependent operator. To this end we introduce the concept of Tykhonov triple, provide three relevant examples, then we state and prove the corresponding well-posedness results. This allows us to deduce various corollaries which illustrate the continuous dependence of the solution with respect to the data. Our results provide mathematical tools in the analysis of a large number of history-dependent problems which arise in Mechanics, Physics and Engineering Sciences. To give an example, we consider a mathematical model which describes the equilibrium of a viscoelastic body in frictionless contact with a rigid foundation.
Key words: history-dependent variational inequality / Tykhonov triple / Tykhonov well-posedness / newline viscoelastic material / Signorini problem
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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