Waiting time phenomena forced by critical boundary conditions in classical diffusion problems

This paper revisits some very classical initial-boundary value problems for parabolic equations, providing simple examples in which the occurrence of flux discontinuities at the boundary when the unknown function reaches some critical value may give rise to a waiting time phenomenon. A physical interpretation could be a modification of the surface of the considered body taking place at the mentioned critical value, affecting the way the body interacts with the surroundings. The waiting time, whose length (finite or infinite) is a priori unknown allows the system to evolve gradually through the critical state. Some numerical simulations are also presented.