### Set-valued perturbation for time dependent subdifferential operator

DOI: http://dx.doi.org/10.12775/TMNA.2015.054

#### Abstract

In a separable Hilbert space, we consider an evolution inclusion involving time-dependent subdifferential of a proper convex lower semicontinuous function with a set-valued perturbation depending on both time and state variable. We prove, under a compactness condition on the perturbation, that there exists at least one absolutely continuous solution.

#### Keywords

Evolution problem, time dependent subdifferential operator, upper hemicontinuous set-valued perturbation, absolutely continuous solution

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