Asymptotic Drying of Gelatin in Photographic Film

In this paper we study the asymptotic behavior of the solution for the diffusion equation ∂u/∂t = ∂[exp(−1/u)∂(u/(1 + u))/∂x]/∂x with mixed nonlinear boundary conditions. The problem arises in the study of the diffusion of water in the gelatin layer of photographic film. We show that there exists a unique positive solution which converges to 0 asymptotically.