A class of non-linear transport and diffusion models implemented with non-linear boundary conditions was derived. Mathematical tools to treat the initial-boundary value problems were developed, based on generalized collocation methods, focused on the treatment of non-linear boundary conditions in one space dimension. Applications refer to a problem of interest in applied sciences.

Transport-Diffusion Models with Nonlinear Boundary Conditions and Solution by Generalized Collocation Methods. E.De Angelis, R.Revelli, L.Ridolfi: Computers & Mathematics with Applications, 2009, 58[3], 558-65