Construction of Polynomial Solutions to Some Boundary Value Problems for Poisson's Equation

被引：24
|
作者：
Karachik, V. V. [1 ]
机构：
[1] So Ural State Univ, Chelyabinsk 454080, Russia
来源：
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2011年 / 51卷 / 09期
关键词：
Almansi formula; polynomial solutions; Dirichlet problems for Poisson's equation; third boundary value problem for Poisson's equation;
D O I：
10.1134/S0965542511090120
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A polynomial solution of the inhomogeneous Dirichlet problem for Poisson's equation with a polynomial right-hand side is found. An explicit representation of the harmonic functions in the Almansi formula is used. The solvability of a generalized third boundary value problem for Poisson's equation is studied in the case when the value of a polynomial in normal derivatives is given on the boundary. A polynomial solution of the third boundary value problem for Poisson's equation with polynomial data is found.
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页码：1567 / 1587
页数：21
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