Numerical computations for the spatial segregation limit of some 2D competition-diffusion systems

We provide a set of numerical simulations for the spatial segregation limit of two diffusive Lotka-Volterra models in presence of strong competition and inhomogeneous Dirichlet boundary conditions. We consider the classical non-variational quadratic coupling as well as a cubic coupling which makes the problem variational. For both cases we perform a numerical investigation of the limiting density distributions, the front tracking, the segregation rate and the dependence of the shape of the segregated regions upon the size of diffusion coefficients. This approach can be easily extended to the multi-species multi-dimensional case.