Spatial decay in a cross-diffusion problem

Abstract

In this paper, the authors investigate the decay of end effects for a cross-diffusion problem defined on a semi-infinite cylindrical region. With homogeneous Dirichlet or Neumann conditions prescribed on the lateral surface of the cylinder, it is shown that for fixed finite time and under certain restrictions on the coefficients, solutions decay point-wise as the distance d from the finite end of the cylinder tends to infinity at least of order e(-kappa d2). Under less restrictive conditions, it is shown that solutions decay in L-2 at least as fast as e(-kappa d). In both cases, kappa is a computable function of time.