On the Solutions of a Porous Medium Equation with Exponent Variable. (1st August 2019)

• Record Type: Journal Article
• Authors: Zhan, Huashui
• Other Names: Fragnelli Genni Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2019(2019)
• Publication Date: 2019-08-01
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2019/9290582
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : The paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of weak solutions is studied. In some special cases, the stability of weak solutions can be proved without any boundary value condition.