A nonlinear diffusion system with convection Original Research Article

This paper deals with a coupled nonlinear diffusion system with convection. A characteristic matrix equation covering all the six nonlinear exponents of the system is introduced to get a simple description for the blow-up criteria of the system. In addition, the influence of the four coefficients of the diffusion and the convection as well as the geometry of ΩΩ on global boundedness or not of the solutions is shown clearly, especially for the situation with the critical sign of the characteristic parameters.