Wave breaking in the periodic integrable Hunter-Saxton equation with a dispersive term
Received:January 05, 2019  Revised:March 31, 2019
Key Word: Hunter-Saxton equation, integrable equation, blow-up, wave-breaking  
Fund ProjectL:National Natural Science Foundation of China (No.11561059)
Author NameAffiliationE-mail
Ying Zhang School of Mathematics and Statistics,Tianshui Normal University zwbandzy@163.com 
Ruichang Pei School of Mathematics and Statistics,Tianshui Normal University  
Dewang Cui School of Mathematics and Statistics,Tianshui Normal University  
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Abstract:
      Consider 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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