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
* e-mail: email@example.com
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.