Cauchy Problem For A System Of Dynamics Of Biological Groups

This paper is devoted to the Cauchy problem of the degenerate quasilinear parabolic systems with p-Laplace operator in the principal part.The nonlinear diffusion systems what we have discussed may describe the interacting evolution of two biological groups better than the linear ones.Moreover,some phenomena,such as competition, extinction,expansion of the living spaces of the species may be described by this systems.In this paper, we establish the existence and uniqueness of week solutions for our systems. Especially,some interesting properties,such as non-extinction,coexistence, expansion of the living spaces, etc.are proved.