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Keywords:
subdifferential; relaxation theorem; Filippov-Gronwall inequality; lower semicontinuous multifunction; continuous selector; weak norm
subdifferential; relaxation theorem; Filippov-Gronwall inequality; lower semicontinuous multifunction; continuous selector; weak norm
Summary:
In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdifferentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the “Filippov-Gronwall” inequality and using it, we prove the parametric relaxation theorem. An example of a parabolic distributed parameter system is also worked out in detail.
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