Time-dependent subdifferential evolution inclusions and optimal control

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dc.contributor.author Hu, SC en
dc.contributor.author Papageorgiou, NS en
dc.date.accessioned 2014-03-01T11:45:42Z
dc.date.available 2014-03-01T11:45:42Z
dc.date.issued 1998 en
dc.identifier.issn 0065-9266 en
dc.identifier.uri https://dspace.lib.ntua.gr/xmlui/handle/123456789/37567
dc.subject subdifferentials en
dc.subject multivalued mappings en
dc.subject differential inclusions en
dc.subject extremal solutions en
dc.subject variational inequalities en
dc.subject optimal control en
dc.subject relaxability en
dc.subject.classification Mathematics en
dc.subject.other RIGHT-HAND SIDE en
dc.subject.other RELAXED TRAJECTORIES en
dc.subject.other BANACH-SPACES en
dc.subject.other SOLUTION SETS en
dc.subject.other EQUATIONS en
dc.subject.other CONVERGENCE en
dc.subject.other RELAXATION en
dc.subject.other OPERATORS en
dc.subject.other APPROXIMATIONS en
dc.title Time-dependent subdifferential evolution inclusions and optimal control en
heal.type other en
heal.language English en
heal.publicationDate 1998 en
heal.abstract The purpose of this paper is to study from many different viewpoints evolution inclusions and optimal control problems involving time dependent subdifferential operators. Throughout this work we take a special interest in the t-dependence of the functional phi(t, x), involved in the subdifferential. We employ a condition that allows the domain dom phi(t,.) to vary regularly without precluding the possibility that dom phi(t,.) boolean AND dom(s,.) = 0 for t not equal s. Hence our formulation is general enough to incorporate problems with time varying constraints (obstacles), In section 3, we deal with evolution inclusions. In 3.1 we prove two existence theorems; one for a nonconvex valued orientor field F and the other for a convex valued one, In 3.2 we look for extremal solution, In 3.3 we relate the nonconvex and the convexified evolution inclusions. In 3.4 we study the dependence of the solution set in all the data of the problem. In 3.5 we prove a parametrized version of the relaxation result which is done using a parametrized analogue of the "Filippov-Gronwall" inequality. In 3.6 we establish the path-connectedness of the solution set. In section 4, we focus our attention to the optimal control of systems monitored by subdifferential evolution inclusions, In 4.1 we develop an existence theory. In 4.2 we study three different formulations of the relaxed problem and make comparisons. In 4.3 we investigate the well-posedness of the optimal control problem. In 4.4 we compare the concepts of relaxability and well-posedness and show that under mild conditions on the data they are in fact equivalent. In section 5, we present several examples of systems monitored by p.d.e's which illustrate the applicability of our abstract results. en
heal.publisher AMER MATHEMATICAL SOC en
dc.identifier.isi ISI:000073546300001 en
dc.identifier.volume 133 en
dc.identifier.issue 632 en
dc.identifier.spage VIII en
dc.identifier.epage + en

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