Blow-Up Rate and Profile for a Degenerate Parabolic System Coupled via Nonlocal Sources

摘要

This paper deals with a degenerate parabolic system with nonlocal nonlinear sources, subject to homogeneous Dirichlet condition. We establish the critical exponent as well as the blow-up rate and profile for the system. It is interesting to observe that the blow-up exponent is determined by the interaction between the nonlinear diffusion and the nonlinear reaction, while the blow-up rate is independent of the nonlinear diffusion. The effects from the nonlocality of the sources are substatial.