### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 471-497 |

Number of pages | 27 |

Journal | Communications In Mathematical Physics |

Volume | 266 |

Issue number | 2 |

DOIs | |

State | Published - Sep 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Communications In Mathematical Physics*, vol. 266, no. 2, pp. 471-497. https://doi.org/10.1007/s00220-006-0047-8

**Conservative solutions to a nonlinear variational wave equation.** / Bressan, Alberto; Zheng, Yuxi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Conservative solutions to a nonlinear variational wave equation

AU - Bressan, Alberto

AU - Zheng, Yuxi

PY - 2006/9/1

Y1 - 2006/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33746215045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746215045&partnerID=8YFLogxK

U2 - 10.1007/s00220-006-0047-8

DO - 10.1007/s00220-006-0047-8

M3 - Article

AN - SCOPUS:33746215045

VL - 266

SP - 471

EP - 497

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -