Critical exponents for a nonlinear diffusion system

This paper deals with critical exponents for a nonlinear diffusion system with inner absorptions and coupled nonlinear boundary flux. A precise analysis of the interactions among the multi-nonlinearities in the system is given to determine the critical exponents, which are simply described via the signs of a pair of parameters (ρ1,ρ2)(ρ1,ρ2) solving the characteristic algebraic system introduced: the solutions are non-global for large initial data if 1/ρ11/ρ1 or 1/ρ2>01/ρ2>0, and global if 1/ρ1,1/ρ2<01/ρ1,1/ρ2<0; while in the critical case of (1/ρ1,1/ρ2)=(0,0)(1/ρ1,1/ρ2)=(0,0) the solutions can be both global and non-global, depending on the geometry and the size of the domain ΩΩ.