A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions

By Stanislav N. Antontsev, S. Shmarev. 2005

335 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/83edd8e11b87f512a4e40c525d6e6c1405d99e01

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Overview of differential equations with non-standard growth (2010, background): “[43] Antontsev, S.; Shmarev, S.: Parabolic equations with anisotropic nonstandard growth conditions.”
Hölder estimates for parabolic p(x, t)-Laplacian systems (2012, background): “Other applications (in the case of equations) stem from flows in porous media [3,22].”
Solutions of nonlinear problems involving p(x)-Laplacian operator (2015, background): “Theseproblemsappear in themodelling of stationary thermo-rheological viscous ows of non-Newtonian uids, in themathematical description of the processes ltration of an ideal barotropic gas through a porousmedium and in the study of electrorheological uids or elastic mechanics [1, 2, 11, 16, 22].”
On a p(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{p(x)}$$\end{document}-biharmonic problem with singula (2017, background): “We also refer to elastic mechanics (see [29]), stationary thermo-rheological viscous flows of nonNewtonian fluids, image processing (see [6]) as well as the mathematical description of the filtration process of a barotropic gas through a porous medium (see [1]).”
Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian (2013, background): “Problems with variable exponent growth conditions also appear in the mathematical modelling of stationary thermo-rheological viscous flows of non-Newtonian fluids and in the mathematical description of the processes filtration of ideal barotropic gas through a porous medium 3 , 4 .”