Reactio-diffusion on the field-road space ℝ^{2}_{+}

We perform here numerical simulations on the field-road space ℝ×ℝ_{+}

Hair Trigger Effect (systematic invasion when a KPP reaction acts in the field). We used an implicit Euler scheme for the time derivative and P1 FEM to solve the elliptic problem at each iteration. (FreeFem code here)

Simulation of the associated diffusive problem and decay rate of the L^{∞} norm of the solution. We used an implicit Euler scheme for the time derivative and a centered-three-points scheme for the Laplacian. (Matlab code here)