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  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11561059) and Tianshui Normal University `QinglanTalents' Project.
Author NameAffiliation
Ying ZHANG School of Mathematics and Statistics, Tianshui Normal University, Gansu 741001, P. R. China 
Ruichang PEI School of Mathematics and Statistics, Tianshui Normal University, Gansu 741001, P. R. China 
Dewang CUI School of Mathematics and Statistics, Tianshui Normal University, Gansu 741001, P. R. China 
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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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