Author(s)

Qitong Ou, Huashui Zhan

School of Applied Mathematics, Xiamen University of Technology, Xiamen, China.

In this paper, the existence and uniqueness of local solutions to the initial and boundary value problem of a class of parabolic system related to the p-Laplacian are studied. The regularization method is used to construct a sequence of approximation solutions, with the help of monotone iteration technique, then we get the existence of solution of a regularized system. By the use of a standard limiting process, the existence of the local solutions of the system is obtained. Finally, the uniqueness of the solution is also proven.

Existence, Uniqueness, Evolution, P-Laplacian, Parabolic System

Ou, Q. and Zhan, H. (2016) Local Solutions to a Class of Parabolic System Related to the P-Laplacian. Advances in Pure Mathematics, 6, 868-877. doi: 10.4236/apm.2016.612065.