Weak Solutions to a Nonlinear Variational Wave Equation |
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| Authors: | Ping Zhang Yuxi Zheng |
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| Institution: | (1) Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080, P. R. China e-mail: zp@math03.math.ac.cn, CN;(2) Department of Mathematics The Pennsylvania State University University Park PA 16802 e-mail: yzheng@math.psu.edu, CN |
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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 L
p
spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation.
(Accepted July 9, 2002) Published online December 3, 2002
Dedicated to Tony Zhang on his seventieth birthday Communicated by C. M. Dafermos |
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