论文标题
Fokas对角度化
Fokas diagonalization
论文作者
论文摘要
最近将解决线性初始边界值问题的方法重新成熟为真实的光谱变换方法。作为重新制定的一部分，阐明了频谱转化对角线的确切含义。这项工作集中在有限间隔网络上的两个点初始边界值问题和接口问题上。在目前的工作中，我们通过三个示例将这些结果扩展到新的问题类别：半芬纳域上的问题，非本地边界条件的问题以及部分微分方程具有混合衍生物的问题。我们表明，通过FOKAS变换方法得出的转换对具有相同的fokas对角线化属性，我们认为这种弱的对角线化属性正是确保确保光谱变换方法成功所需的。
A method for solving linear initial boundary value problems was recently reimplemented as a true spectral transform method. As part of this reformulation, the precise sense in which the spectral transforms diagonalize the underlying spatial differential operator was elucidated. That work concentrated on two point initial boundary value problems and interface problems on networks of finite intervals. In the present work, we extend these results, by means of three examples, to new classes of problems: problems on semiinfinite domains, problems with nonlocal boundary conditions, and problems in which the partial differential equation features mixed derivatives. We show that the transform pair derived via the Fokas transform method features the same Fokas diagonalization property in each of these new settings, and we argue that this weak diagonalization property is precisely that needed to ensure success of a spectral transform method.
