Free boundary problems and spreading of species

Abstract

In this talk I will first review some classical results on the spreading phenomena determined by reaction diffusion equations over the entire ${ℝ}^N$. Then I will report some recent results obtained by the speeker and his collaborators based on these equations over an expanding domain $\Omega \left(t\right)$, where the free boundary $\partial \Omega \left(t\right)$ evolves according to the Stefan condition. Comparison of the recent results with the classical ones will be discussed.