Abstract: This paper aims at a weak coupling evolution p-Laplacian system with the first initial and boundary value conditions. Under appropriate hypotheses, the method of regularization is used to construct a sequence of solutions with the help of monotone iteration technique and the solution to the regularized system can be found. Then the existence of solutions to the evolution p-Laplacian system is obtained by a standard limiting process. Finally, the uniqueness of the solution can be proven by integral method.

Key words: existence, uniqueness, quasilinear, degenerate, parabolic systems