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Differential Variational–hemivariational Inequalities with Application to Contact Mechanics by Stanisław Migórski; Dong-ling Cai; Sylwia Dudek is a Mathematics article available to read on EtoBox.

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In this paper we study a dynamical system which consists of the Cauchy problem for a nonlinear evolution equation of first order coupled with a nonlinear time-dependent variational–hemivariational inequality with constraint in Banach spaces. The evolution equation is considered in the framework of evolution triple of spaces, and the inequality which involves both the convex and nonconvex potentials. We prove existence of solution by the Kakutani–Ky Fan fixed point theorem combined with the Minty formulation and the theory of hemivariational inequalities. We illustrate our findings by examining a nonlinear quasistatic elastic frictional contact problem for which we provide a result on existence of weak solution.

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Author

Stanisław Migórski; Dong-ling Cai; Sylwia Dudek

Publisher

Elsevier BV

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)