A general class of second order differential equations

  • Francisco-Javier Sayas
Chapter
First Online:
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 50)

Abstract

In this short chapter we introduce some elementary tools of evolution equations which will be applied to the analysis of time domain potentials and integral operators. Most of these results in the abstract treatment of evolution equations can be obtained with elementary tools of the theory of strongly continuous semigroups of operators (of groups of isometries actually). An introduction to semigroup techniques applied to partial differential equations can be found in [58, Chapter 4] or [44], with a very general treatment given in [71]. The theory of semigroups of operators is rarely part of the mathematical toolbox for users of boundary integral equations. This is the reason why we include a self-contained approach in Appendix B using a simple point of view, namely the method of separation of variables.

Keywords

Bilinear Form Boundary Integral Equation Dirichlet Form Rigid Motion Continuous Semigroup 
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Bibliography

  1. 44.
    K.-J. Engel, R. Nagel, A Short Course on Operator Semigroups. Universitext (Springer, New York, 2006)Google Scholar
  2. 58.
    S. Kesavan, Topics in Functional Analysis and Applications (Wiley, New York, 1989)Google Scholar
  3. 71.
    A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol. 44 (Springer, New York, 1983)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Francisco-Javier Sayas
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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