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The generalized Hunter-Saxton system. (English) Zbl 1223.35092
Summary: A new system of equations generalizing the Hunter-Saxton system [the author, Discrete Contin. Dyn. Syst., Ser. B 12, No. 3, 647--656 (2009; Zbl 1176.35028)] is derived and investigated. In the periodic setting, we show that there exist local solutions for which we provide sufficient conditions in order that they stay bounded or blow up in finite time; on the real line, we construct a class of global weak solutions.

35B44Blow-up (PDE)
35B35Stability of solutions of PDE
35D30Weak solutions of PDE
35G25Initial value problems for nonlinear higher-order PDE
35L67Shocks and singularities
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