Time-dependent subdifferential evolution inclusions and optimal control

Hu, SC; Papageorgiou, NS

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	DIFFERENTIAL-INCLUSIONS	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
heal.journalName	MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY	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