Lipschitzian semigroups and abstract functional differential equations |
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Authors: | Xueli Song Jigen Peng |
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Institution: | a Department of Mathematics and Information Science, Chang’an University, Xi’an 710064, China b Department of Mathematics, Xi’an Jiaotong University, Xi’an 710049, China |
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Abstract: | The paper is devoted to studying an abstract functional differential equation by a nonlinear semigroup approach. We first prove in details the equivalence of the well posedness of an abstract functional differential equation and an associated abstract Cauchy problem in the sense of strong solutions. Secondly, a sufficient condition is derived for well posedness of the abstract functional differential equation. Thirdly, we present principles of linearized stability for the abstract functional differential equation. Finally, the results obtained are applied to a reaction-diffusion equation with delays. |
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Keywords: | 34k20 34k30 |
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