Blowup issues for a class of nonlinear dispersive wave equations

Abstract:

In this paper we consider the nonlinear dispersive wave equation on the real line, ut-utxx+[f(u)]x-[f(u)]xxx+[g(u)+f″(u)2ux2]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 u0 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→+∞ and x→-∞. © 2014 Elsevier Inc.

Año de publicación:

2014

Keywords:

• Wave breaking
• Rod equation
• Shallow water
• Camassa-Holm

Fuente:

scopus