| 张颖,裴瑞昌,崔德旺.带色散项的周期可积Hunter-Saxton方程的波的破裂[J].数学研究及应用,2019,39(5):517~528 |
| 带色散项的周期可积Hunter-Saxton方程的波的破裂 |
| Wave Breaking in the Periodic Integrable Hunter-Saxton Equation with a Dispersive Term |
| 投稿时间：2019-01-05 修订日期：2019-04-12 |
| DOI：10.3770/j.issn:2095-2651.2019.05.008 |
| 中文关键词: Hunter-Saxton方程 可积方程 爆破 波的破裂 |
| 英文关键词:Hunter-Saxton equation integrable equation blow-up wave-breaking |
| 基金项目:国家自然科学基金(Grant No.11561059),天水师范学院“青蓝”人才工程基金资助. |
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| 中文摘要: |
| 本文考虑一个带色散项的可积Hunter-Saxton方程的周期柯西问题.首先,我们得出该模型的强解的一个精确的爆破机制.其次,利用守恒量和特征方法,分别建立了有限时间内强解的爆破发生的充分条件.最后,给出了强解的爆破率. |
| 英文摘要: |
| Considered here is the periodic Cauchy problem for an integrable Hunter-Saxton equation with a dispersive term. Firstly, we derive a precise blow-up criterion of strong solutions to the equation. Secondly, sufficient conditions guaranteeing the development of breaking waves in finite time are demonstrated by applying some conservative quantities and the method of characteristics, respectively. Finally, the exact blow-up rate is determined. |
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