Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations
Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations
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DOI：
10.1016/j.aml.2019.02.003
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
A. Rybkin
中科院分区：
文献类型：
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作者：
A. Rybkin
我们关注源自非特征流形的一阶线性偏微分方程的双曲系统。我们提出了一种简单但有效的方法，将此类初始条件转换为标准初始条件（即在初始时刻指定解时）。然后我们展示我们的方法如何应用于流体力学。更具体地说，我们针对具有非零初速度的任意形状的倾斜海湾中的长波爬升问题提出了完整的解决方案。
We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the solution is specified at an initial moment of time). We then show how our method applies in fluid mechanics. More specifically, we present a complete solution to the problem of long waves run-up in inclined bays of arbitrary shape with nonzero initial velocity.