Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
Well-posed two-point initial-boundary value problems with arbitrary boundary conditions
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具有任意边界条件的适定两点初边值问题
DOI：
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发表时间：
2011
影响因子：
0.8
通讯作者：
David A. Smith
中科院分区：
文献类型：
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作者：
David A. Smith
摘要本文研究了矩形1-空间1-时间区域上任意空间阶线性发展方程的初边值问题，该问题具有任意线性边界条件。我们给出了一个新的特征的边界条件，指定适定的问题，使用Fokas的变换方法。我们还给出了一个充分条件，保证解决方案可以表示为一个系列。相关的条件，解析在无穷远的某些亚纯函数在特定部门，是显着更具体和更容易测试比以前的标准，根据存在的容许函数。
Abstract We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.