  This paper is concerned with the Cauchy problem for a two-component
Degasperis-Procesi system. Firstly, the local well-posedness for this system in
the nonhomogeneous Besov spaces is established. Then the precise blow-up
scenario for strong solutions to the system is derived. Finally, two new
blow-up criterions and the exact blow-up rate of strong solutions to the system
are presented.
