Open AccessOn the Solutions of a Porous Medium Equation with Exponent Variable
Author(s) -
Mingguang Li
Publication year - 2019
Publication title -
discrete dynamics in nature and society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.264
H-Index - 39
eISSN - 1607-887X
pISSN - 1026-0226
DOI - 10.1155/2019/9290582
Subject(s) - exponent , monotone polygon , mathematics , variable (mathematics) , boundary value problem , porous medium , mathematical analysis , stability (learning theory) , nonlinear system , boundary (topology) , porosity , physics , materials science , computer science , geometry , philosophy , linguistics , quantum mechanics , machine learning , composite material
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.