Partial differential hemivariational inequalities

By Zhenhai Liu, Shengda Zeng, Dumitru Motreanu. Advances in Nonlinear Analysis, 2018

108 citations recorded by the source corpus.

Abstract The aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution equations and hemivariational inequalities. First, we introduce the concept of strong well-posedness for mixed variational quasi hemivariational inequalities and establish metric characterizations for it. Then we show the existence of solutions and meaningful properties such as measurability and upper semicontinuity for the solution set of the mixed variational quasi hemivariational inequality associated to the partial differential hemivariational inequality. Relying, on these properties we are able to prove the existence of mild solutions for partial differential hemivariational inequalities. Furthermore, we show the compactness of the set of the corresponding mild trajectories.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ab142798dd3a9943f1ea532f0034a7fc91ad983e

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In Computational Theory and Mathematics

1. Shengda Zeng
2. Stanislaw Migórski
3. Zhenhai Liu
4. Anna Ochal
5. Mircea-Traian Sofonea

In Mechanics of Materials

1. Shengda Zeng
2. Zhenhai Liu
3. Stanislaw Migórski
4. Anna Ochal
5. Mircea-Traian Sofonea

Citations in the corpus

• A class of fractional differential hemivariational inequalities with application to contact problem (2018, background): “[29,30] have initiated the study on differential hemivariational inequalities in Banach spaces.”