Time dependent nonlinear Cauchy problems in Banach spaces

Fitzgibbon, W. E.

doi:10.1090/S0002-9939-1972-0308539-7

Time dependent nonlinear Cauchy problems in Banach spaces
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by W. E. Fitzgibbon PDF

Proc. Amer. Math. Soc. 36 (1972), 525-530 Request permission

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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