Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator☆

By A. Kulig, Stanislaw Migórski. 2012

51 citations recorded by the source corpus.

Abstract The paper deals with second order nonlinear evolution inclusions and their applications. We study evolution inclusions involving a Volterra-type integral operator, which are considered within the framework of an evolution triple of spaces. First, we deliver a result on the unique solvability of the Cauchy problem for the inclusion by combining a surjectivity result for multivalued pseudomonotone operators and the Banach contraction principle. Next, we provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Finally, we consider a dynamic frictional contact problem of viscoelasticity for materials with long memory and indicate how the result on evolution inclusion is applicable to the model of the contact problem.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/06939c03d7a378c37b9d1561e436b9d2779528fb