Nonconvex evolution inclusions generated by time-dependent subdifferential operators
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,r we show that under a Lipschitz condition on th...
Published in: | Journal of Applied Mathematics and Stochastic Analysis |
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Main Authors: | , , |
Format: | Article in Journal/Newspaper |
Language: | unknown |
Published: |
1999
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Subjects: | |
Online Access: | http://dspace.lib.ntua.gr/handle/123456789/13262 https://doi.org/10.1155/S1048953399000222 |
Summary: | 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,r 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. ©1999 by North Atlantic Science Publishing Company. |
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