A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems

We study the existence of segregated solutions to a class of reaction-diffusion systems with strong interactions, arising in many physical applications. These special solutions are obtained as weak limits of minimizers of a family of perturbed functionals. We prove some a priori estimates through a minimization procedure which is nonstandard in the parabolic theory: our approach is purely variational and all the information is encoded in the family of functionals we consider.