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Zbl 1242.35179
Kulig, Anna; Migórski, Stanisław
Solvability and continuous dependence results for second order nonlinear evolution inclusions with a Volterra-type operator. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 13, 4729-4746 (2012). ISSN 0362-546X

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 2000:: *35L90 Abstract hyperbolic evolution equations
35R70 PDE with multivalued right-hand sides
45P05 Integral operators
47H04 Set-valued operators
47H05 Monotone operators (with respect to duality)
74H20 Existence of solutions
74H25 Uniqueness of solutions

Keywords: evolution inclusion; pseudomonotone operator; Volterra-type operator; multifunction; hyperbolic; contact problem; hemivariational inequality; viscoelasticity

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