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Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator. (English) Zbl 1242.35179
Summary: 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.
MSC:
35L90Abstract hyperbolic equations
35R70PDE with multivalued right-hand sides
45P05Integral operators
47H04Set-valued operators
47H05Monotone operators (with respect to duality) and generalizations
74H20Existence of solutions for dynamical problems in solid mechanics
74H25Uniqueness of solutions for dynamical problems in solid mechanics
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