Boundedness and almost periodicity in time of solutions of evolutionary variational inequalities

In this paper existence theorems are obtained for the solutions of abstract parabolic variational inequalities, which are bounded with respect to time (in the Stepanov and $L^\infty$ norms). The regularity and almost periodicity properties of such solutions are studied. Theorems are also established concerning their solvability in spaces of Besicovitch almost periodic functions. The majority of the results are obtained without any compactness assumptions.
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