Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator |
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Authors: | Anna Kulig,Stanisław Migó rski |
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Affiliation: | Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. ?ojasiewicza 6, 30-348 Krakow, Poland |
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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. |
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Keywords: | 35L90 35R70 45P05 47H04 47H05 74H20 74H25 |
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