On a Partial Boundary Value Condition of a Porous Medium Equation with Exponent Variable. (14th March 2020)

• Record Type: Journal Article
• Authors: Zhan, Huashui
• Other Names: Fragnelli Genni Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2020(2020)
• Publication Date: 2020-03-14
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2020/2929045
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : The initial-boundary value problem of a porous medium equation with a variable exponent is considered. Both the diffusion coefficient a x, t and the variable exponent p x, t depend on the time variable t, and this makes the partial boundary value condition not be expressed as the usual Dirichlet boundary value condition. In other words, the partial boundary value condition matching up with the equation is based on a submanifold of ∂ Ω × 0, T . By this innovation, the stability of weak solutions is proved.