A Class of History-Dependent Systems of Evolution Inclusions with Applications

Abstract: This paper is devoted to studying a system of coupled nonlinear first order history-dependent evolution inclusions in the framework of evolution triples of spaces. The multivalued terms are of the Clarke subgradient or of the convex subdifferential form. Using a surjectivity result for multivalued maps and a fixed point argument for a history-dependent operator, we prove that the system has a unique solution. We conclude with two examples of an evolutionary differential variational-hemivariational inequality and of a dynamic frictional contact problem in mechanics, which illustrate the abstract results.