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Existence and Compactness of Solution Semiflows

  • Jianhong Wu
Chapter
  • 560 Downloads
Part of the Applied Mathematical Sciences book series (AMS, volume 119)

Abstract

The purpose of this chapter is to establish the existence and compactness of solution semiflows defined by a class of semilinear functional differential equations. We will start with the case where the linear operator generates a C0-semigroup of bounded linear operators and the nonlinear term satisfies a global Lipschitz condition. We will then indicate how to relax this global Lipschitz condition by imposing compactness on the linear semigroup. In the final section, we will derive a class of semilinear functional differential equations of neutral type from a continuous array of coupled lossless transmission lines and we will obtain the basic existence-uniqueness result for such a class of equations.

Keywords

Bounded Linear Operator Mild Solution Functional Differential Equation Reaction Diffusion Equation Analytic Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Jianhong Wu
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

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