Deterministic and stochastic front propagation (10w5073)
Xavier Cabre (ICREA and Universitat Politecnica de Catalunya)
Francois Hamel (Universite d'Aix-Marseille)
Jeremy Quastel (University of Toronto)
Jean-Michel Roquejoffre (Universite Paul Sabatier Toulouse III)
Lenya Ryzhik (Stanford University)
Front propagation, driven by reaction, diffusion and transport, appears as one of the central features in various phenomena in combustion, chemistry, biology and physics. Because of its ubiquitous character, the study
of front dynamics is carried out in almost all branches of science.
The mathematical questions that arise in front propagation, and in particular, in reaction-diffusion equations often turn out to be at the leading edge of nonlinear analysis. Methods from nonlinear partial differential equations, dynamical systems and ordinary differential equations are often all required in the modern treatment of reaction-diffusion equations. Moreover, stochastic aspects become more and more important, both in order to take into account the complexity of the
physical and biological environments, and to obtain reduced stochastic models due to the complexity of the full but intractable models.
The workshop will focus on the following main issues: (i) new notions of propagation, (ii) singular limits and free boundary problems, including homogenization, (iii) non-local effects, (iv) the de Giorgi conjecture and (v) entropy methods.