Interactions among multi-nonlinearities in a nonlinear diffusion system with absorptions and nonlinear boundary flux Original Research Article

This paper deals with a nonlinear diffusion system with inner absorptions and coupled nonlinear boundary conditions. Two parameters, which solve an introduced matrix equation covering all the eight nonlinear exponents of the system, are used to get a simple description for the interactions among the multi-nonlinearities in the system. Blow-up or not of the solutions is determined by the signs of the two parameters. In order to obtain the critical properties of the solutions for the critical sign of the parameters, some further analysis on the absorption coefficients and the geometry of Ω is given in addition to the discussion for the eight nonlinear exponents in the system.