Wave-breaking phenomena for the nonlocal Whitham-type equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Ma, Feiyao¹  Liu, Yue^1,2  Qu, Changzheng¹ 

[1] Ningbo Univ, Dept Math, Ningbo 315211, Zhejiang, Peoples R China

[2] Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA

关键词: Wave-breaking;    Whithatn-type equations;    Camnssa-Holm equation;    mu-Camassa-Holm equation;    Degasperis-Procesi equation;    Hyperelastic rod equation;   

DOI  :  10.1016/j.jde.2016.08.027

来源: Elsevier

【 摘 要 】

In this paper, the formation of singularities for the nonlocal Whitham-type equations is studied. It is shown that if the lowest slope of flows can be controlled by its highest value with the bounded Whitham-type integral kernel initially, then the finite-time blow-up will occur in the form of wave-breaking. This refined wave-breaking result is established by analyzing the monotonicity and continuity properties of a new system of the Riccati-type differential inequalities involving the extremal slopes of flows. Our theory is illustrated via the Whitham equation, Camassa-Holm equation, Degasperis-Procesi equation, and their A-versions as well as hyperelastic rod equation. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free