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

A. B. Antonevich; D. A. Lyakhov

doi:10.1134/S0012266112080071

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 language	English (US)
Pages (from-to)	1119-1126
Number of pages	8
Journal	Differential Equations
Volume	48
Issue number	8
DOIs	https://doi.org/10.1134/S0012266112080071
State	Published - Nov 2012
Externally published	Yes

ASJC Scopus subject areas

Analysis
General Mathematics

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title = "Dirichlet problem in the ball for an equation with a delta-like coefficient",

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.",

author = "Antonevich, {A. B.} and Lyakhov, {D. A.}",

year = "2012",

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N2 - 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.

AB - 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.

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DO - 10.1134/S0012266112080071

M3 - Article

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VL - 48

SP - 1119

EP - 1126

JO - Differential Equations

JF - Differential Equations

IS - 8

ER -

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

Abstract

ASJC Scopus subject areas

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