Wave Breaking in the Periodic Integrable Hunter-Saxton Equation with a Dispersive Term |
Received:January 05, 2019 Revised:April 12, 2019 |
Key Words:
Hunter-Saxton equation integrable equation blow-up wave-breaking
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Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11561059) and Tianshui Normal University `QinglanTalents' Project. |
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Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2019.05.008 |
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