Critical exponents and lower bounds of blow-up rate for a reaction-diffusion system

This paper is concerned with a reaction-diffusion system with absorption terms under Dirichlet boundary conditions, modelling the cooperative interaction of two diffusion biological species. By constructing blow-up sub-solutions and bounded super-solutions, we obtain the optimal conditions on the exponent of reaction and absorption terms for the existence or nonexistence of global solutions. Moreover, for a special case, we derive the lower bound estimates of blow-up rate.