Modified Fundamental Solutions

  • Gavin R. Thomson
  • Christian Constanda


As we have seen in Chapters 6 and 7, the integral equations of the second kind that arise in the classical direct and indirect boundary integral formulations may have multiple solutions for certain values of the oscillation frequency ω. In Chapter 7 it was shown that, for the exterior problems, a unique solution does exist if we operate with a special pair of integral equations. The question is, can the matrix of fundamental solutions D ω (x,y) be modified so that we may obtain a single secondkind equation for each of the exterior problems, which has a unique solution for all values of ω?


Integral Equation Fundamental Solution Helmholtz Equation Reciprocity Relation Unique Solvability 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.A.C.C.A.GlasgowUK
  2. 2.Department of Mathematical and Computer SciencesThe University of TulsaTulsaUSA

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