Weak solutions to a nonlinear variational wave equation

Ping Zhang; Yuxi Zheng

doi:10.1007/s00205-002-0232-7

Weak solutions to a nonlinear variational wave equation

Ping Zhang
, Yuxi Zheng

Mathematics

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

63 Scopus citations

Abstract

We establish the global existence of weak solutions to the Cauchy problem for a nonlinear variational wave equation, where the wave speed is a given monotone function of the wave amplitude. The equation arises in modeling wave motions of nematic liquid crystals, long waves on a dipole chain, and a few other fields. We use the Young-measure method in the setting of L^p spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation.

Original language	English (US)
Pages (from-to)	303-319
Number of pages	17
Journal	Archive for Rational Mechanics and Analysis
Volume	166
Issue number	4
DOIs	https://doi.org/10.1007/s00205-002-0232-7
State	Published - Mar 2003

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-002-0232-7

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abstract = "We establish the global existence of weak solutions to the Cauchy problem for a nonlinear variational wave equation, where the wave speed is a given monotone function of the wave amplitude. The equation arises in modeling wave motions of nematic liquid crystals, long waves on a dipole chain, and a few other fields. We use the Young-measure method in the setting of Lp spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation.",

author = "Ping Zhang and Yuxi Zheng",

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AU - Zhang, Ping

AU - Zheng, Yuxi

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N2 - We establish the global existence of weak solutions to the Cauchy problem for a nonlinear variational wave equation, where the wave speed is a given monotone function of the wave amplitude. The equation arises in modeling wave motions of nematic liquid crystals, long waves on a dipole chain, and a few other fields. We use the Young-measure method in the setting of Lp spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation.

AB - We establish the global existence of weak solutions to the Cauchy problem for a nonlinear variational wave equation, where the wave speed is a given monotone function of the wave amplitude. The equation arises in modeling wave motions of nematic liquid crystals, long waves on a dipole chain, and a few other fields. We use the Young-measure method in the setting of Lp spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation.

UR - https://www.scopus.com/pages/publications/0037934336

UR - https://www.scopus.com/pages/publications/0037934336#tab=citedBy

U2 - 10.1007/s00205-002-0232-7

DO - 10.1007/s00205-002-0232-7

M3 - Article

AN - SCOPUS:0037934336

SN - 0003-9527

VL - 166

SP - 303

EP - 319

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 4

ER -

Weak solutions to a nonlinear variational wave equation

Abstract

All Science Journal Classification (ASJC) codes

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