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Prof. Stanislaw Migorski
Jagiellonian University in Krakow, Poland
Evolutionary Variational-Hemivariational Inequalities with Memory and their Applications
In this talk we provide results on existence and uniqueness of so- lution to the evolutionary second order variational-hemivariational inequalities. We deal with a class of abstract problems which contain two potentials, at least one of them is convex, and a memory operator. The main tools are the Clarke generalized gradient, a theorem on surjectivity of a multivalued pseudomono- tone operator, and a ┬»xed point argument. The results are generalizations of some earlier contributions obtained for quasistatic problems. Then, we provide an application of abstract results to study the existence and uniqueness of the weak solutions to nonsmooth dynamic contact problems of mechanics. We con- sider the nonlinear constitutive viscoelastic law with a long memory term and general nonmonotone and multivalued subdi®erential boundary conditions for the contact and friction.
Professor Stanislaw Migorski is a Full Professor of Mathematical Sciences and the Chair Professor in the Chair of Optimization and Control at the Jagiellonian University in Krakow, Poland. He is the co-author of three monographs and more than 100 publications in refereed journals. Dr. Migorski has published numerous articles on his research interests in Control Theory, Differential Equations, Nonlinear Functional Analysis, Calculus of Variations and Applications. An invited speaker and a chairman at many international conferences and congresses in Australia, Brazil, Canada, China, Europe, Japan, USA, he served also as a member of several program committees. Project coordinator of international consortia among European Union, China and USA.
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