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Relaxation of optimal control problems driven by nonlinear evolution equations

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Dedicated to Professor Meir Shillor on the occasion of his 70th birthday

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  • We consider a nonlinear optimal control problem with dynamics described by a nonlinear evolution equation defined on an evolution triple of spaces. Both the dynamics and the cost functional are not convex and so an optimal pair need not exist. For this reason using tools from multivalued analysis and from convex analysis, we introduce a relaxed version of the problem. No Young measures are involved in our relaxation method. We show that the relaxed problem is admissible.

    Mathematics Subject Classification: 49J20, 49J35, 34G20.

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