Abstract functional-differential equations and reaction-diffusion systems

Martin, R. H.; Smith, H. L.

doi:10.1090/S0002-9947-1990-0967316-X

Abstract functional-differential equations and reaction-diffusion systems
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by R. H. Martin and H. L. Smith

Trans. Amer. Math. Soc. 321 (1990), 1-44

DOI: https://doi.org/10.1090/S0002-9947-1990-0967316-X

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Abstract:

Several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a Banach space setting. The ideas are applied to reaction-diffusion systems that have time delays in the nonlinear reaction terms. The techniques presented here include differential inequalities, invariant sets, and Lyapunov functions, and therefore they provide for a wide range of applicability. The results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays.

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