Singular and rarefactive solutions to a nonlinear variational wave equation

Ping Zhang, Zheng Yuxi

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Abstract

Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.

Original languageEnglish (US)
Article number0252-9599(2001)02-0159-12
Pages (from-to)159-170
Number of pages12
JournalChinese Annals of Mathematics. Series B
Volume22
Issue number2
DOIs
StatePublished - Jan 1 2001

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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