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Global Conservative Solutions to a Nonlinear Variational Wave Equation

Alberto Bressan·Yuxi Zheng
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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.

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Alberto Bressan, Yuxi Zheng. 2005-02-02. Global Conservative Solutions to a Nonlinear Variational Wave Equation. https://doi.org/10.1007/s00220-006-0047-8

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