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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.

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
Full Text: DOI
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