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arXiv · 1211.7197

Semigroups and linear partial differential equations with delay

András Bátkai·Susanna Piazzera
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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.

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András Bátkai, Susanna Piazzera. 2012-11-30. Semigroups and linear partial differential equations with delay. https://doi.org/10.1006/jmaa.2001.6705

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