Differential Equations

, Volume 48, Issue 8, pp 1119–1126 | Cite as

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

  • A. B. Antonevich
  • D. A. Lyakhov
Partial Differential Equations


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.


Closed Form Unit Ball Dirichlet Problem Delta Function Choose Method 
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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • A. B. Antonevich
    • 1
  • D. A. Lyakhov
    • 1
  1. 1.Belarus State UniversityMinskBelarus

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