On H 2-solutions for a Camassa-Holm type equation

Abstract

Camassa-Holm type equations arise as models for the unidirectional propagation of shallow water waves over a flat bottom. They also describe finite length, small amplitude radial deformation waves in cylindrical compressible hyperelastic rods. Under appropriate assumption on the initial data, on the time TT, and on the coefficients of such equation, we prove the well-posedness of the classical solutions for the Cauchy problem.

Keywords

• existence
• uniqueness
• stability
• camassa-holm type equation
• cauchy problem
• 35g25
• 35k55