Abstract
In this paper, we study a class of evolution subdifferential inclusions involving history-dependent operators. We improve our previous theorems on existence and uniqueness and produce a continuous dependence result with respect to weak topologies under a weaker smallness condition. Two applications are provided to a frictional viscoelastic contact problem with long memory, and to a nonsmooth semipermeability problem.
Highlights
We study a class of the Cauchy problems for evolution inclusions of subdifferential type in the framework of evolution triple of spaces
The problem has been studied in [21] without the convex subdifferential term and under the sign condition for the nonconvex potential, and in [8], where reformulated as a variational–hemivariational inequality, has been analyzed under a restrictive smallness hypothesis on the constants involved in operators A and ∂J [see problem (1.1), (1.2) below]
We provide a new application of our results to a semipermeability problem with nonmonotone and possibly multivalued subdifferential boundary conditions
Summary
We study a class of the Cauchy problems for evolution inclusions of subdifferential type in the framework of evolution triple of spaces. The problem has been studied in [21] without the convex subdifferential term and under the sign condition for the nonconvex potential, and in [8], where reformulated as a variational–hemivariational inequality, has been analyzed under a restrictive smallness hypothesis on the constants involved in operators A and ∂J [see problem (1.1), (1.2) below] We replace this restriction by a weaker condition and further examine the continuous dependence for such inclusions which was not studied before. Note that the continuous dependence result in weak topologies obtained in this paper can be used in analysis of various optimization and optimal control problems for variational and variational–hemivariational inequalities with history-dependent operators
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