Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes

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• 作者：S. R. Garifullina (1)
  E. Yu. Postnikova (2)
  
• 关键词：asymptotic expansion ; small parameter ; boundary value problem for Laplace’s equation ; method of matched asymptotic expansions
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2013
• 出版时间：November 2013
• 年：2013
• 卷：53
• 期：11
• 页码：1591-1606
• 全文大小：
• 作者单位：S. R. Garifullina (1)
  E. Yu. Postnikova (2)
  
  1. Bashkir State University, ul. Zaki Validi 32, Ufa, 450074, Bashkortostan, Russia
  2. Chelyabinsk State University, ul. Brat’ev Kashirinykh 129, Chelyabinsk, 454001, Russia
  
• ISSN：1555-6662

文摘

A boundary value problem for Laplace’s equation in a bounded domain with two small holes is considered. Third-type boundary conditions are set on the boundaries of the holes. A Neumann condition is specified on the outer boundary of the domain. A uniform asymptotic approximation of the solution is constructed and justified up to an arbitrary power of a small parameter.