Solvability of the moisture transport model for porous materials

TL;DR

This paper proves the existence and uniqueness of solutions for a nonlinear moisture transport model in porous materials, addressing boundary condition challenges with a fixed point theorem approach.

Contribution

It introduces a modified boundary condition to handle the nonlinear parabolic equation and establishes rigorous mathematical proof of solvability.

Findings

Existence and uniqueness of solutions are proven.

The model's boundary condition issues are effectively addressed.

Mathematical framework applicable to similar nonlinear PDEs.

Abstract

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.