A Nonlinear Diffusion System with Coupled Nonlinear Boundary Flux (Journal of Partial Differential Equations, 2009)
This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources (positive for the first and negative for the second), where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem.
Keywords: Critical exponents; nonlinear diffusion; inner absorptions; nonlinear boundary flux; blow-up; global solutions; characteristic algebraic system