Global weak solutions and blow-up structure for the Degasperis-Procesi equation

摘要

In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions. (c) 2006 Elsevier Inc. All rights reserved.