Existence and Representation Theorems for a Semilinear Sobolev Equation in Banach Space

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Abstract
This is the publisher’s final pdf. The published article is copyrighted by the Society for Industrial and Applied Mathematics and can be found at: http://epubs.siam.org/loi/sjmaah.An existence theory is developed for a semilinear evolution equation in Banach space\ud which is modeled on boundary value problems for partial differential equations of Sobolev type. The\ud operators are assumed to be measurable and to satisfy coercive estimates which are not necessarily\ud uniform in their time dependence, and to satisfy Lipschitz conditions on the nonlinear term. Applications\ud are briefly indicated

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