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\r\ntwo diffusive Lotka-Volterra models in presence of strong competition and inhomogeneous\r\nDirichlet boundary conditions. We consider the classical non-variational quadratic coupling\r\nas well as a cubic coupling which makes the problem variational. For both cases we\r\nperform a numerical investigation of the limiting density distributions, the front tracking,\r\nthe segregation rate and the dependence of the shape of the segregated regions upon the\r\nsize of diffusion coefficients. This approach can be easily extended to the multi-species\r\nmulti-dimensional case.