Nonconvex evolution inclusions generated by time-dependent subdifferential operators

Kate Arseni-Benou, Nikolaos Halidias and Nikolaos S. Papageorgiou

International Journal of Stochastic Analysis, 1999, vol. 12, 1-20

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.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:687971

DOI: 10.1155/S1048953399000222

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