On convergence of numerical algorithm of a class of the spatial segregation of reaction-diffusion system with two population densities

摘要

Recently, much interest has gained the numerical approximation of equationsof the Spatial Segregation of Reaction-diffusion systems with m populationdensities. These problems are governed by a minimization problem subject to theclosed but non-convex set. In the present work we deal with the numericalapproximation of equations of stationary states for a certain class of theSpatial Segregation of Reaction-diffusion system with two population densitieshaving disjoint support. We prove the convergence of the numerical algorithmfor two competing populations with non-negative internal dynamics $f_i(x)\geq0.$ At the end of the paper we present computational tests.