This project will follow two lines of investigation into problems of applied mathematics. The first is that of understanding certain mathematical models for phase transition phenomena. The problems have a variational structure and involve the study of distinguished solutions for elliptic or parabolic equations with small diffusion coefficients. The second category of work will concentrate on evolution systems that are not necessarily of variational type and which preserve order. One main objective is to determine asymptotic properties of all solutions. A common theme which ties the research together is that the problems deal with reaction-diffusion mechanisms and that the analysis employs stability considerations. From the applications point of view, the first project seeks to model certain observable patterns either as stable equilibria or as unstable manifolds of equilibria; the second seeks to exclude the possibility of stable chaos for classes of forced systems and to establish very regular behavior criteria.
