Asymptotics near the shore for 2D shallow water over sloping planar bottom

摘要

A two-dimensional nonlinear run-up problem is studied for the special case of planar bottom. For two-dimensional shallow water equations, the Cauchy problem is considered. For initial data the wave generated by localized source is considered when it comes close to the shoreline. Asymptotics are constructed using perturbation theory and the Carrier-Greenspan transform for the coordinate x normal to the shoreline. Obtained formulas are explicit and can be easily computed using parametrically defined functions.