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Local Solutions to a Class of Parabolic System Related to the P-Laplacian
School of Applied Mathematics, Xiamen University of Technology, Xiamen, China
School of Applied Mathematics, Xiamen University of Technology, Xiamen, China
- 1 School of Applied Mathematics, Xiamen University of Technology, Xiamen, China
- 2 School of Applied Mathematics, Xiamen University of Technology, Xiamen, China
Advances in Pure Mathematics·Volume 06 (2016)·Pages 868–877·Published 8 November 2016·DOI10.4236/apm.2016.612065
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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.
KeywordsExistenceUniquenessEvolutionP-LaplacianParabolic System
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