## Atelier des doctorants 07/12

The field-road diffusion model: fundamental solution and asymptotic behavior

Lundi 9 mai 2022, 14:30 à 15:30

Salle de séminaire

Samuel Tréton

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.