, Volume 48, Issue 8, pp 1119-1126
Date: 15 Nov 2012

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

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Abstract

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 Russian Text © A.B. Antonevich, D.A. Lyakhov, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 8, pp. 1133–1139.