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Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data
The Cauchy problem is considered for the two-dimensional wave equation with velocity $c=\sqrt x_1$ on the half-plane $\{x_1\geq 0,x_2\}$, with initial data localized in a neighborhood of the point $(1,0)$. This problem serves as a model problem in the theory of beach run-up of long small-amplitude surface waves excited by …