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

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

Hair Trigger Effect VS Extinction. We compare here in terms of invasion/extinction a reaction with Allee effect (difficulty of the population to grow at low density) with a KPP type reaction (the more the population density is low, the more it grows fast). An Euler scheme is used for the time derivative (implicit for the Laplacians and explicit for the nonlinearity); the Laplacians are discretized with three and five point centered schemes.

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 three and five centered points schemes for the Laplacians. (Matlab code here)