KTH/SU Mathematics Colloquium
2005-04-27
Henri Berestycki (EHESS - Paris)
Reaction - diffusion equations and propagation phenomena
Front or pulse propagation phenomena arise in a variety of contexts
such as flames, chemical reactions, phase transitions, biological
invasions and even social behaviors. Equations and systems of
reaction-diffusion (possibly with transport or advection terms) have
long been used to describe these phenomena. In this lecture, after
recalling these models, I will survey some of the classical results
dealing with the homogeneous reaction-diffusion equation, focusing on
propagation of fronts and asymptotic speed of spreading. Then I will
present some generalizations regarding propagation in heterogeneous
media. I will discuss in particular biological invasions in periodic
heterogeneous media as well as a model for species facing a climate
change. The results emphasize some new effects due to heterogeneity.