Global Conservative Solutions to a Nonlinear Variational Wave Equation

Alberto Bressan; Yuxi Zheng

doi:10.1007/s00220-006-0047-8

Global Conservative Solutions to a Nonlinear Variational Wave Equation

Analysis of PDEs 2009-11-11 v1

Authors: 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.

Keywords

cauchy problem nonlinear wave equations weak solutions

Cite

@article{arxiv.math/0502058,
  title  = {Global Conservative Solutions to a Nonlinear Variational Wave Equation},
  author = {Alberto Bressan and Yuxi Zheng},
  journal= {arXiv preprint arXiv:math/0502058},
  year   = {2009}
}

Comments

32 pages, 6 figures

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