On nonexisting solutions for Dirichlet problem and MAC

机译：关于Dirichlet问题和MAC的不存在的解决方案

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The Dirichlet problem for Laplace equation is considered. The nonexisting solution of the problem for unbounded domain is analyzed. If the domain is a ring then the solution exist. But if the outer boundary of a ring tends to infinity then the solution of the Dirichlet problem does not exist for different boundary values on the inner and outer boundaries. The method of additional conditions (MAC) can give bounded solutions of Dirichlet problem in the case of angle and corner singularities in classical consideration of the problem. In this paper MAC is applied to obtain the physically understandable solution also in this case of classically nonexisting solution. The solution could be considered as the solution of a bad posed Cauchy problem for Laplace equation.

机译：考虑了拉普拉斯方程的Dirichlet问题。分析了无界域问题的不存在的解决方案。如果域是环，则解决方案存在。但是，如果环的外边界趋于无穷大，则对于内边界和外边界上的不同边界值，狄利克雷特问题的解决方案将不存在。附加条件的方法（MAC）可以在角度和角奇异性的情况下经典地考虑该问题，从而给出Dirichlet问题的有界解。在本文中，在经典不存在的情况下，MAC也用于获得物理上可理解的解决方案。该解决方案可以看作是Laplace方程的一个有害的Cauchy问题的解决方案。

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来源
《Finite differences, finite elements, finite volumes, boundary elements》|2011年|p.132-135|共4页
会议地点 Paris(FR);Paris(FR)
作者
IGOR NEYGEBAUER;
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作者单位

University of Dodoma Department of Mathematics and Statistics P.O.Box 259, Dodoma TANZANIA;

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会议组织
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
singularity; laplace equation; method of additional conditions;

机译：奇点拉普拉斯方程附加条件的方法;

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2. Equivalence of weak Dirichlet's principle, the method of weak solutions and Perron's method towards classical solutions of Dirichlet's problem for harmonic functions [J] . Christian G. Simader Mathematische Nachrichten . 2006,第4期

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4. On nonexisting solutions for Dirichlet problem and MAC [C] . IGOR NEYGEBAUER WSEAS International Conference on Finite Differences - Finite Elements - Finite Volumes - Boundary Elements . 2011

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On nonexisting solutions for Dirichlet problem and MAC

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