Singular and rarefactive solutions to a nonlinear variational wave equation

Ping Zhang; Zheng Yuxi

doi:10.1142/S0252959901000152

Singular and rarefactive solutions to a nonlinear variational wave equation

Ping Zhang, Zheng Yuxi

Mathematics

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

27 Scopus citations

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 language	English (US)
Article number	0252-9599(2001)02-0159-12
Pages (from-to)	159-170
Number of pages	12
Journal	Chinese Annals of Mathematics. Series B
Volume	22
Issue number	2
DOIs	https://doi.org/10.1142/S0252959901000152
State	Published - Jan 1 2001

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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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.",

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