Hysteresis and Hemivariational Inequalities: Semilinear Case

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Abstract

In this paper we consider semilinear parabolic boundary value problems having nonsmooth and nonmonotone behaviour and memory effects. The mathematical problem can be formulated and studied by using the notions of hemivariational inequality (based on the generalized gradient in the sense of F.H. Clarke) and the hysteresis operator. We establish two general existence results for such problems. Applications from mechanics illustrate the theory.

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