Global Conservative Solutions to a Nonlinear Variational Wave Equation

Abstract

We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt}-c(u)(c(u)u_x{)}_x=0$, for initial data of finite energy. Here $c(\cdot )$ is any smooth function with uniformly positive bounded values.

32 pages, 6 figures

References in corpus (1)

• An integrable shallow water equation with peaked solitons

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