A gradient flow for the porous medium equations with Dirichlet boundary conditions

Journal of Mathematical Analysis and Applications 2026 Open access

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Authors: Dongkwang ‍Kim, Dowan Koo, Geuntaek Seo
DOI: 10.1016/j.jmaa.2026.131102
Cited by: 1
References: 23

Abstract

We consider the gradient flow structure of the porous medium equations with non-negative constant Dirichlet boundary conditions. We construct weak solutions to the equations via the minimizing movement scheme by considering an entropy functional with respect to 𝑊 ⁢ 𝑏 2 distance, which is a modified Wasserstein distance introduced by Figalli and Gigli (2010) [9] . Furthermore, the constructed solutions are characterized as curves of maximal slope in a suitable sense.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Geometric Analysis and Curvature Flows Advanced Mathematical Modeling in Engineering

Publication details

Journal / source
Journal of Mathematical Analysis and Applications
Publisher
Elsevier BV
Volume
566
Issue
1
Pages
131102–131102
Publication date
18 September 2026
Language
EN