Semigroups and linear partial differential equations with delay

Abstract

We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm continuity of the solutions. Applications to a reaction-diffusion equation with delay are given.

Journal of Mathematical Analysis and Applications Vol. 264, 2001, pp. 1-20

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