On the rigorous foundations of the Fokas method for linear elliptic partial differential equations
On the rigorous foundations of the Fokas method for linear elliptic partial differential equations
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DOI：
10.1098/rspa.2011.0478
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发表时间：
2012-05-08
影响因子：
3.5
通讯作者：
Ashton, A. C. L.
中科院分区：
文献类型：
--
作者：
Ashton, A. C. L.
在本文中，我们解决了一些严格的基础上的Fokas方法，限制注意力的边界值问题的线性椭圆型偏微分方程的有界凸域。该方法的中心对象是全局关系，它是谱傅里叶空间中的积分方程，将给定的边界数据与未知的边界值耦合起来。利用多变量复分析的技巧，我们证明了全局关系的解提供了相应边值问题的解，并且全局关系的解是唯一的。结果适用于任何数量的空间维度和各种边值问题。
In this paper, we address some of the rigorous foundations of the Fokas method, confining attention to boundary value problems for linear elliptic partial differential equations on bounded convex domains. The central object in the method is the global relation, which is an integral equation in the spectral Fourier space that couples the given boundary data with the unknown boundary values. Using techniques from complex analysis of several variables, we prove that a solution to the global relation provides a solution to the corresponding boundary value problem, and that the solution to the global relation is unique. The result holds for any number of spatial dimensions and for a variety of boundary value problems.