Dirichlet problem in the ball for an equation with a delta-like coefficient

A. B. Antonevich, D. A. Lyakhov

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We study the Dirichlet problem in the ball for the Helmholtz equation with an additional term in the form of the product by the delta function. The additional term is approximated by the simplest integral expression, and the solution of the original equation is defined as the limit of solutions of the regularized equations. We obtain exact solutions depending on the chosen method of approximation.

Original languageEnglish (US)
Pages (from-to)1119-1126
Number of pages8
JournalDifferential Equations
Issue number8
StatePublished - Nov 1 2012
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

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