Abstract:

Aiming at the extinction properties of solutions to a fast diffusion system with nonlinear sources, the authors first established the local existence of weak solutions to this problem as well as the uniqueness under certain conditions, and then gave some sufficient conditions for the solutions to vanish in finite time with the help of the theories of invariant regions for ODES, integral estimates  and Sobolev embedding theorems. The results show that the solutions may vanish in finite time when the source terms are suitably weak.

Key words: fast diffusion system, nonlinear source, extinction