EXISTENCE AND STRONG RELAXATION THEOREMS FOR NONLINEAR EVOLUTION INCLUSIONS
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概要
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In this paper we study nonlinear evolution inclusions defined on a Gelfand triple of spaces. First we prove an existence and compactness result for the set of solutions of the "convex" problems. Then we look at extrenal solutions and show that under reasonable hypotheses such solutions exist. Moreover if the orientor field (multivalued perturbation term) is h-Lipschitz in the state-variable, we show that the set of extrenal solutions is dense in the solution set of the convexi ed problem ("strong relaxation theorem"). We also show that the solution set is compact in ＄C(T, H)＄ if and only if the orientor field is convex-valued. Finally we present two examples of parabolic distributed parameter systems which illustrate the applicability of our abstract results.
- Yokohama City University and Yokohama National Universityの論文
- 1995-00-00
Yokohama City University and Yokohama National University | 論文
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