Global existence and uniqueness of weak solutions to a one-dimensional moisture transport model for porous materials

This paper deals with the moisture transport model for porous materials,$ \dfrac{ \partial v}{ \partial t} = \dfrac{ \partial}{ \partial x} \left(\alpha \dfrac{ \partial v}{ \partial x} + \lambda(\psi^{-1}(v)) \dfrac{ \partial g}{ \partial x}\right), \quad t \in (0,T),\ x \in (0,1) $under the boundary condition $ \frac{ \partial v}{ \partial x} = -\psi'(\psi^{-1}(v))\frac{ \partial g}{ \partial x} $ for $ t \in (0,T) $, $ x \in \{0,1\} $ and the initial condition, where $ \alpha>0 $ is some constant, $ \psi, \lambda, g $ are functions satisfying some conditions and $ T>0 $. This model represents the moisture transport in porous media occupying a one-dimensional interval. The purpose of this paper is to prove existence and uniqueness of weak solutions to this initial-boundary value problem.