Blowup issues for a class of nonlinear dispersive wave equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Brandolese, Lorenzo¹  Cortez, Manuel Fernando¹ 

[1] Univ Lyon 1, CNRS, Inst Camille Jordan, UMR 5208, F-69622 Villeurbanne, France

关键词: Rod equation;    Camassa-Holm;    Shallow water;    Wave breaking;   

DOI  :  10.1016/j.jde.2014.03.008

来源: Elsevier

【 摘 要 】

In this paper we consider the nonlinear dispersive wave equation on the real line, u(t) - u(txx) + [f(u)](x) - [f(u)](xxx) + [g(u) + f ''(u)/2u(x)(2)](x) = 0, that for appropriate choices of the functions f and g includes well known models, such as Dai's equation for the study of vibrations inside elastic rods or the Camassa-Holm equation modelling water wave propagation in shallow water. We establish a local-in-space blowup criterion (i.e., a criterion involving only the properties of the data u(0) in a neighborhood of a single point) simplifying and extending earlier blowup criteria for this equation. Our arguments apply both to the finite and infinite energy cases, yielding the finite time blowup of strong solutions with possibly different behavior as x -> infinity and x -> -infinity. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free