The dissertation deals with second order nonlinear evolution inclusions, hyperbolic hemivariation... more The dissertation deals with second order nonlinear evolution inclusions, hyperbolic hemivariational inequalities and their applications. First, we study a class of the evolution inclusions involving a Volterra integral operator and considered within the framework of an evolution triple of spaces. Combining a surjectivity result for multivalued pseudomonotone operators and the Banach Contraction Principle, we deliver a result on the unique solvability of the Cauchy problem for the inclusion. We also provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Next, we consider a class of hyperbolic hemivariational inequalities and embed these problems into a class of evolution inclusions with the multivalued term generated by the generalized Clarke subdifferential for nonconvex and nonsmooth superpotentials. Finally, we study a dynamic frictional contact problem of viscoelasticity with a general constitutive la...
The dissertation deals with second order nonlinear evolution inclusions, hyperbolic hemivariation... more The dissertation deals with second order nonlinear evolution inclusions, hyperbolic hemivariational inequalities and their applications. First, we study a class of the evolution inclusions involving a Volterra integral operator and considered within the framework of an evolution triple of spaces. Combining a surjectivity result for multivalued pseudomonotone operators and the Banach Contraction Principle, we deliver a result on the unique solvability of the Cauchy problem for the inclusion. We also provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Next, we consider a class of hyperbolic hemivariational inequalities and embed these problems into a class of evolution inclusions with the multivalued term generated by the generalized Clarke subdifferential for nonconvex and nonsmooth superpotentials. Finally, we study a dynamic frictional contact problem of viscoelasticity with a general constitutive la...
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