On permanent and breaking waves in hyperelastic rods and rings

Abstract:

We prove that the only global strong solution of the periodic rod equation vanishing in at least one point (t0,x0)∈R+×S1 is the identically zero solution. Such conclusion holds provided the physical parameter γ of the model (related to the Finger deformation tensor) is outside some neighborhood of the origin and applies in particular for the Camassa-Holm equation, corresponding to γ. = 1. We also establish the analogue of this unique continuation result in the case of non-periodic solutions defined on the whole real line with vanishing boundary conditions at infinity. Our analysis relies on the application of new local-in-space blowup criteria and involves the computation of several best constants in convolution estimates and weighted Poincaré inequalities. © 2014 Elsevier Inc.

Año de publicación:

2014

Keywords:

• minimization
• Wave-breaking
• Rod equation
• Weighted poincaré inequality
• Shallow water
• Camassa-Holm
• Blowup
• Compressible rod

Fuente:

scopus