Geodesic
Parametrized relaxation for evolution inclusions of the subdifferential type
Archivum mathematicum, Tome 31 (1995) no. 1, pp. 9-28

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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.
Classification : 34A60, 34G20, 46N20, 49J52, 93C20
Keywords: subdifferential; relaxation theorem; Filippov-Gronwall inequality; lower semicontinuous multifunction; continuous selector; weak norm 
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     author = {Papageorgiou, Nikolaos S.},
     title = {Parametrized relaxation for evolution inclusions of the subdifferential type},
     journal = {Archivum mathematicum},
     pages = {9--28},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {1995},
     mrnumber = {1342371},
     zbl = {0839.34075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1995__31_1_a1/}
}
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Papageorgiou, Nikolaos S. Parametrized relaxation for evolution inclusions of the subdifferential type. Archivum mathematicum, Tome 31 (1995) no. 1, pp. 9-28. http://geodesic.mathdoc.fr/item/ARM_1995__31_1_a1/