A Priori Estimates for Operational Differential Inclusions

Frankowska, H. (1988). A Priori Estimates for Operational Differential Inclusions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-88-126

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Abstract

The author proves a set-valued Gronwall lemma and a relaxation theorem for the semilinear differential inclusion x' E Ax + F(t,x), x(0)=x_0 where A is the infinitesimal generator of a C_0-semigroup on a separable Banach space X and F : [0,T] x X --> X is a set-valued map. This result is important for investigation of many futures of semilinear inclusions, for instance, infinitesimal generators of reachable sets, variational inclusions, etc.

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