Attractors and asymptotic behavior for reaction diffusion problems in unbounded domains

Attractors and asymptotic behavior for reaction diffusion problems in unbounded domains

In this talk we will review the difficulties found when studying the asymptotic dynamics and attractors for reaction diffusion problems in unbounded domains. We will show some previous results and we will show the underlying dissipative mechanisms which allow to obtain sufficient compactness of the solutions.Thiscompactnessallowsustoderive theexistenceoftheattractor, for which we will show that there exist extremal equilibria. Our analysis is carried out in Lebesque spaces, L^p, and in locally uniform spaces. This allows to handle large classes of problems.

We will also show how these results apply to logistic type equations that appear in numerous concrete models.