10.1016/0022-1236(72)90079-1

Generating an evolution system in a class of uniformly convex Banach spaces

Abstract

AbstractLet E be a Banach space such that both E and its dual space are uniformly convex. In this paper we consider the problem of existence of solutions to the system u′(t) ϵ A(t) u(t) where A(t) is a dissipative subset of E × E for each t in [a, b]. It is also assumed that the family {A(t) : t ϵ [a, b]} satisfies a demiclosed condition and a directional growth condition. Using the technique developed here, we are able to characterize densely defined generators of strongly continuous nonlinear semigroups

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This paper was published in Elsevier - Publisher Connector .

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