arXiv subjects

Akiko Morimura

Publications and source records attributed to Akiko Morimura.

3 recordsLinked to original sources

arXiv2025

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

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.

math.AP↗

arXiv2025

Convergence of approximate solutions constructed by the finite volume method for the moisture transport model in porous media

We consider the initial-boundary value problem for a nonlinear parabolic equation in the one-dimensional interval. This problem is motivated by a mathematical model for moisture transport in porous media. We establish the uniqueness of weak solutions to the problem by using the dual equation method. Moreover, we prove the convergence of approximate solutions constructed with the finite volume method.

math.AP↗

arXiv2024

Solvability of the moisture transport model for porous materials

We consider an initial and boundary value problem invoked from the mathematical model for moisture transport in porous materials. Because of the difficulty appearing in the boundary condition, we have changed it and obtain the nonlinear parabolic equation with the nonlinear boundary condition in the one-dimensional interval. The main result of this paper is to prove existence and uniqueness of solutions to the problem by applying the standard fixed point theorem argument.

math.AP↗