Properties of the solutions to the two-component bb-family systems

In this paper, some properties of the solutions are considered to the two-component bb-family systems, which cover the two-component Camassa–Holm equation and the two-component Degasperis–Procesi equation. This paper is concerned with some aspects of the existence of global solutions, persistence properties and propagation speed. One first discusses the local well-posedness and blow-up scenario, then, establishes the sufficient conditions on the global existence of the solutions. Finally, the persistence properties and propagation speed of strong solutions will also be investigated.