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Conservative Solutions to a Nonlinear Variational Wave Equation

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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(·) is any smooth function with uniformly positive bounded values.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA

    Alberto Bressan & Yuxi Zheng

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  1. Alberto Bressan
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  2. Yuxi Zheng
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Correspondence to Alberto Bressan.

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Communicated by P. Constantin

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Bressan, A., Zheng, Y. Conservative Solutions to a Nonlinear Variational Wave Equation. Commun. Math. Phys. 266, 471–497 (2006). https://doi.org/10.1007/s00220-006-0047-8

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