On the Compactness of the Nonlinear Evolution Operator in a Banach Space |
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Authors: | Calvert, Bruce Kartsatos, Athanassios G. |
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Affiliation: | Department of Mathematics and Statistics, The University of Auckland Private Bag, Auckland, New Zealand Department of Mathematics, University of South Florida Tampa, Florida 33620, USA |
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Abstract: | Let X be a real Banach space and let A(t): X 2x be dissipativefor all t(0, T). Assume that {A(t)} generates an evolution operatorU(t, s) of type (D, , f). Necessary and sufficient conditionsare given for the compactness of U(t, s) for 0 s < t <T. |
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