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.