An initial-boundary value problem describing moisture transport in porous media: Existence of strong solutions and an error estimate for a finite volume scheme

Evolution equations and control theory 2026 Open access

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Authors: Akiko Morimura, Toyohiko Aiki
DOI: 10.3934/eect.2026036
Cited by: 0
References: 9

Abstract

We consider an initial-boundary value problem motivated by a mathematical model of moisture transport in porous media. We establish the existence of strong solutions and provide an error estimate for the approximate solutions constructed by the finite volume method. In the proof of the error estimate, the Gagliardo–Nirenberg type inequality for the difference between a continuous function and a piecewise constant function plays an important role.

Fields of Study & Subjects

Differential Equations and Boundary Problems Nonlinear Partial Differential Equations Advanced Numerical Methods in Computational Mathematics

Publication details

Journal / source
Evolution equations and control theory
Volume
21
Issue
0
Pages
112–130
Publication date
1 January 2026
Language
EN