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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| Institution: | 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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