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Existence and relaxation results for nonlinear second order evolution inclusions

Stanisław Migórski — 1995

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we study nonlinear evolution inclusions associated with second order equations defined on an evolution triple. We prove two existence theorems for the cases where the orientor field is convex valued and nonconvex valued, respectively. We show that when the orientor field is Lipschitzean, then the set of solutions of the nonconvex problem is dense in the set of solutions of the convexified problem.

Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

Stanisław Migórski — 2012

Open Mathematics

We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...

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