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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 5364746, 11 pages
https://doi.org/10.1155/2018/5364746
Research Article

The Stability of the Solutions for a Porous Medium Equation with a Convection Term

School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China

Correspondence should be addressed to Miao Ouyang; nc.ude.tumx@gnayuom

Received 28 June 2017; Revised 17 November 2017; Accepted 22 November 2017; Published 10 January 2018

Academic Editor: Guang Zhang

Copyright © 2018 Huashui Zhan and Miao Ouyang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the initial-boundary value problem of a porous medium equation with a convection term. If the equation is degenerate on the boundary, then only a partial boundary condition is needed generally. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of the solutions is studied. In some special cases, the stability can be proved without any boundary value condition.