Singularities of a Variational Wave Equation
Singularities of a Variational Wave Equation
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DOI：
10.1006/jdeq.1996.0111
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发表时间：
1996-07
影响因子：
2.4
通讯作者：
R. Glassey;J. K. Hunter;Yuxi Zheng
中科院分区：
文献类型：
--
作者：
R. Glassey;J. K. Hunter;Yuxi Zheng
摘要本文分析了一个变分非线性波动方程解的奇异性，该方程模拟了大质量液晶指向矢场中的取向波。我们证明了光滑的解决方案在有限时间内发展奇点。我们构造了具有尖点奇点的精确行波解，并用它们来说明能量有界的解序列中振荡的积累和湮灭现象。我们还证明了方程的常数解是非线性不稳定的。
Abstract We analyze several aspects of the singular behavior of solutions of a variational nonlinear wave equation which models orientation waves in a massive nematic liquid crystal director field. We prove that smooth solutions develop singularities in finite time. We construct exact travelling wave solutions with cusp singularities, and use them to illustrate a phenomena of accumulation and annihilation of oscillations in sequences of solutions with bounded energy. We also prove that constant solutions of the equation are nonlinearly unstable.