Fokas method for linear boundary value problems involving mixed spatial derivatives.
Fokas method for linear boundary value problems involving mixed spatial derivatives.
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Fokas 方法用于解决涉及混合空间导数的线性边值问题。
DOI：
10.1098/rspa.2020.0076
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Batal A
中科院分区：
文献类型：
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作者：
Batal A
我们通过统一变换方法（UTM），也称为Fokas方法，得到了半空间上涉及混合空间导数项的线性初边值问题的解表示公式.我们首先实现的方法上的二阶抛物型偏微分方程，在这种情况下，可以替代地消除混合衍生物的变量的线性变化。然后，我们采用的方法，双调和问题，它是不可能的，以消除交叉项通过变量的线性变化。UTM的一个基本组成部分是使用某些不变映射。它在这里示出，这些地图定义良好，提供了某些分析性问题得到适当的解决。
We obtain solution representation formulae for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first implement the method on the second-order parabolic PDEs; in this case one can alternatively eliminate the mixed derivatives by a linear change of variables. Then, we employ the method to biharmonic problems, where it is not possible to eliminate the cross term via a linear change of variables. A basic ingredient of the UTM is the use of certain invariant maps. It is shown here that these maps are well defined provided that certain analyticity issues are appropriately addressed.