Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems

Furi Guo; Jinrong Wang; Jiangfeng Han

doi:10.3934/eect.2021057

Article Contents

2022, Volume 11, Issue 5: 1613-1633. Doi: 10.3934/eect.2021057

This issue Previous Article A special form of solution to half-wave equations Next Article Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses

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
^* Corresponding author: Jinrong Wang

Received: January 31, 2021

Revised: June 30, 2021

Early access: November 2021

Published: October 2022

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Abstract

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.

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Mathematics Subject Classification: 35L15, 35L86, 35L87, 74M10.

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Figure 1. A deformable body in contact with a foundation

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Figure 2. The surface traction $ \boldsymbol f_N $ with impact influence

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