The existence of solutions for drying with coupled phase change in a porous medium

This paper deals with a theoretical mathematical analysis of freezing (desublimation) of moisture in a finite porous medium with a heat flux condition at the boundary. The goal is to generalize [E.A. Santillan Marcus, D.A. Tarzia, Exact solutions for drying with coupled phase-change in a porous medium with a heat flux condition on the surface, Comput. Appl. Math. 22 (2003) 293–311], proving the local existence and uniqueness in time of the solution of this problem. We give the model equations as a free boundary problem, and we prove that the problem is equivalent to a system of Volterra integral equations following the Friedman–Rubinstein’s method given in [A. Friedman, Free boundary problems for parabolic equations, I. Melting of solids, J. Math. Mech. 8 (1959) 499–517]. Then, we prove that the problem has a unique local solution in time by using the Banach contraction theorem.