TITLE:
Local Solutions to a Class of Parabolic System Related to the P-Laplacian
AUTHORS:
Qitong Ou, Huashui Zhan
KEYWORDS:
Existence, Uniqueness, Evolution, P-Laplacian, Parabolic System
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.12,
November
17,
2016
ABSTRACT: 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.