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A Differential Equation Approach to Evolutionary Quasi-Variational Inequalities Arising in Contact Problems

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Abstract

In this paper, we consider a class of evolutionary quasi-variational inequalities arising in the study of contact problems for viscoelastic materials. Based on convex analysis methods and fixed point arguments, we prove the well-posedness and regularity of solutions in a general framework. Then, we establish the correspondence between evolutionary variational inequalities and implicit sweeping processes, which enables us to prove an existence result for history-dependent implicit sweeping processes. Finally, our theoretical results are illustrated with an application to contact mechanics problems for viscoelastic materials with a short memory.

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Acknowledgements

The author wishes to express his gratitude to the anonymous referees for valuable comments that helped improve the manuscript and Pedro Pérez-Aros, from Universidad de O’Higgins, for fruitful discussions concerning the measurability of maximal monotone operators.

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  1. Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

    Emilio Vilches

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  1. Emilio Vilches
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Correspondence to Emilio Vilches.

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This work was partially supported by ANID-Chile under grant Fondecyt de Iniciación N∘11180098.

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Vilches, E. A Differential Equation Approach to Evolutionary Quasi-Variational Inequalities Arising in Contact Problems. Set-Valued Var. Anal 30, 751–768 (2022). https://doi.org/10.1007/s11228-021-00617-w

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