Obstacle type free boundary problems

In this talk we are going to deal with a general class of  the obstacle like free boundary problems . Particularly we will consider the spatial segregation of Reaction-diffusion systems with $m\geq 2$ population densities.  We show that in the case $m=2$, the problem gives rise to the generalized version of the so-called two-phase obstacle problem.

We study finite difference scheme for these type of  problems. The existence and uniqueness of the scheme are proved relying on the  discrete version of a minimization problem.  Some particular convergence results also are presented.