Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. Despite the complex geometry of the problem and the exchange condition, we provide the first explicit expression of its fundamental solution and of the solution to the associated Cauchy problem. The main tool is a Fourier (on the road variable)/Laplace (on time) transform. Furthermore, we estimate the rate of decay of the L^∞ norm of the solution.