# American Institute of Mathematical Sciences

doi: 10.3934/eect.2021057
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## Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems

 1 Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China 2 Department of Mathematics and Statistics, Shanxi Datong University, Datong, Shanxi 037009, China 3 Department of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, China

* Corresponding author: Jinrong Wang

Received  February 2021 Revised  July 2021 Early access November 2021

This paper deals with a class of history-dependent frictional contact problem with the surface traction affected by the impulsive differential equation. The weak formulation of the contact problem is a history-dependent hemivariational inequality with the impulsive differential equation. By virtue of the surjectivity of multivalued pseudomonotone operator theorem and the Rothe method, existence and uniqueness results on the abstract impulsive differential hemivariational inequalities is established. In addition, we consider the stability of the solution to impulsive differential hemivariational inequalities in relation to perturbation data. Finally, the existence and uniqueness of weak solution to the contact problem is proved by means of abstract results.

Citation: Furi Guo, Jinrong Wang, Jiangfeng Han. Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems. Evolution Equations & Control Theory, doi: 10.3934/eect.2021057
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##### References:
The surface traction $\boldsymbol f_N$ with impact influence