Parametrized relaxation for evolution inclusions of the subdifferential type

Papageorgiou, Nikolaos S.

Archivum mathematicum, Tome 31 (1995) no. 1, pp. 9-28

Abstract (VO)

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.

Détail

Classification : 34A60, 34G20, 46N20, 49J52, 93C20
Keywords: subdifferential; relaxation theorem; Filippov-Gronwall inequality; lower semicontinuous multifunction; continuous selector; weak norm

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