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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Time dependent nonlinear Cauchy problems in Banach spaces

Author: W. E. Fitzgibbon
Journal: Proc. Amer. Math. Soc. 36 (1972), 525-530
MSC: Primary 34G05
MathSciNet review: 0308539
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Abstract: The method of product integration is used to obtain solutions to the nonlinear evolution equation $ u'(t) + A(t)u(t) = 0$ where $ \{ A(t):t \in [0,T]\} $ is a family of nonlinear accretive operators mapping a Banach space X to itself. The main requirements are that $ R(I + \lambda A(t)) \supseteq {\text{cl}}(D(A(t))),D(A(t))$ is time independent, the resolvent $ {(I + \lambda A(t))^{ - 1}}x$ satisfies a local Lipschitz condition, and that each A(t) satisfies Condition M.

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Keywords: Nonlinear evolution equation, product integration, accretive operator
Article copyright: © Copyright 1972 American Mathematical Society

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