Existence and Compactness of Solution Semiflows

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


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.


Bounded Linear Operator Mild Solution Functional Differential Equation Reaction Diffusion Equation Analytic Semigroup 
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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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