A quasilinear reaction-diffusion system coupled via nonlocal sources

In this paper, we establish the critical exponent and the blow-up rate for a quasilinear reaction-diffusion system with nonlocal nonlinear sources and inner absorptions, subject to homogeneous Dirichlet conditions and nonnegative initial data. It is found that the critical exponent is determined by the interaction among all the six nonlinear exponents from all the three kinds of the nonlinearities. While the blow-up rate is independent of the nonlinear diffusion exponents due to the effects of the coupled nonlocal sources. Two kinds of characteristic algebraic systems are introduced to get simple descriptions for the critical exponent and the blow-up rate, respectively. We prove moreover that the blow-up could be global due to the nonlocality of the nonlinear sources.