Nonconvex evolution inclusions generated by time-dependent subdifferential operators. (1999)

• Record Type: Journal Article
• Authors: Arseni-Benou, Kate; Halidias, Nikolaos; Papageorgiou, Nikolaos S.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 12:Number 3(1999)
• Page Start: 233
• Page End: 252
• Publication Date: 1999
• Subjects: subdifferential -- strong solution -- strong relaxation -- path-connected -- feedback control system -- parabolic equation; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953399000222
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We consider nonlinear nonconvex evolution inclusions driven by time-varying subdifferentials ∂ ϕ ( t, x ) without assuming that ϕ ( t, . ) is of compact type. We show the existence of extremal solutions and then we prove a strong relaxation theorem. Moreover, we show that under a Lipschitz condition on the orientor field, the solution set of the nonconvex problem is path-connected in C ( T, H ) . These results are applied to nonlinear feedback control systems to derive nonlinear infinite dimensional versions of the “bang-bang principle.” The abstract results are illustrated by two examples of nonlinear parabolic problems and an example of a differential variational inequality.