论文标题
线性边界价值问题的FOKA方法涉及混合空间衍生物
Fokas method for linear boundary value problems involving mixed spatial derivatives
论文作者
论文摘要
我们获得了在半空间上构成的一些线性初始边界值问题的解决方案公式，该空间涉及通过统一变换方法（UTM）（也称为FOKAS方法）的混合空间衍生物项。我们首先在二阶抛物线PDE上实现该方法；在这种情况下，可以通过变量的线性变化来替代消除混合衍生物。然后，我们将方法用于双骑问题问题，在这种情况下，不可能通过变量的线性变化来消除跨期限。 UTM的基本成分是使用某些不变地图。这里表明，只要对某些分析性问题得到适当解决，这些地图是明确的。
We obtain solution representation formulas 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.
