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| Singular and Rarefactive Solutions to a Nonlinear Variational Wave Equation |
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Citation： |
ZHANG Ping,ZHENG Yuxi.Singular and Rarefactive Solutions to a Nonlinear Variational Wave Equation[J].Chinese Annals of Mathematics B,2001,22(2):159~170 |
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Net amount： 946 |
Authors： |
ZHANG Ping; ZHENG Yuxi |
Foundation： |
The first author is supported by the Chinese Youth Foundation and the Innovation Funds of the Chinese Academy of Sciences. The Second author is supported by the Natural Science Foundation DMS-9703711 and K. C. Wang Education Foundation, Hong Kong. |
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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 characteristics. |
Keywords： |
Existence, Young measure, Wave equation |
Classification： |
35Q35, 35L05 |
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