Some properties of solutions to the weakly dissipative Degasperis–Procesi equation

In this paper, we consider the weakly dissipative Degasperis–Procesi equation. The present paper is concerned with some aspects of existence of global solutions, persistence properties and propagation speed. First we try to discuss the local well-posedness and blow-up scenario, then establish the sufficient conditions on global existence of the solution. Finally, persistence properties on strong solutions and the propagation speed for the weakly dissipative Degasperis–Procesi equation are also investigated.