非线性浅水方程的一般初值问题：长波在斜坡上的爬高
General Initial Value Problem for the Nonlinear Shallow Water Equations: Runup of Long Waves on Sloping Beaches and Bays
摘要：
利用Carrier-Greenspan变换[G. Carrier和H. Greenspan，J. Fluid Mech.01，97（1957）]。我们使用泰勒级数近似来处理与变换空间中的曲线上给定的初始条件相关的困难。这将早期的解决方案扩展到具有近岸初始条件，大初始速度和更复杂的U形水深的波浪，并允许在更现实的2-D设置中验证海啸波淹没模型。
英文摘要：
We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier-Greenspan transformation [G. Carrier and H. Greenspan, J. Fluid Mech. 01, 97 (1957)]. We use a Taylor series approximation to deal with the difficulty associated with the initial conditions given on a curve in the transformed space. This extends earlier solutions to waves with near shore initial conditions, large initial velocities, and in more complex U-shaped bathymetries; and allows verification of tsunami wave inundation models in a more realistic 2-D setting.
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