Spatial decay in a cross-diffusion problem

In this paper, the authors investigate the decay of end effectsfor a cross-diffusion problem defined on a semi-infinite cylindricalregion. With homogeneous Dirichlet or Neumann conditions prescribedon the lateral surface of the cylinder, it is shown that forfixed finite time and under certain restrictions on the coefficients,solutions decay point-wise as the distance d from the finiteend of the cylinder tends to infinity at least of order e^–kd2.Under less restrictive conditions, it is shown that solutionsdecay in L₂ at least as fast as e^–kd. In both cases, kis a computable function of time.