On a convective condition in the diffusion of a solvent into a polymer with non-constant conductivity coefficient

We studied a one-dimensional free boundary problem arising in the polymer industry. Imposing a convective boundary condition, the solution has an interesting asymptotic behavior. It is found that the free boundary is bounded by a constant which does not depend on the conductivity coefficient, which holds even if the diffusion process is non-linear. Numerical methods are presented to compute the solutions and to compare with the theoretical results.