Conservative solutions to a nonlinear variational wave equation

Alberto Bressan; Yuxi Zheng

doi:10.1007/s00220-006-0047-8

Conservative solutions to a nonlinear variational wave equation

Alberto Bressan, Yuxi Zheng

Research output: Contribution to journal › Article › peer-review

69 Scopus citations

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	https://doi.org/10.1007/s00220-006-0047-8
State	Published - Sep 2006

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-006-0047-8

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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.",

author = "Alberto Bressan and Yuxi Zheng",

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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.

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Conservative solutions to a nonlinear variational wave equation

Abstract

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