PRopagation in the Equations of Fluids and REaction-Diffusion – PREFERED

Front propagation, driven by reaction, diffusion and transport, appears as one of the central features of combustion, chemistry, biology. Because of its ubiquitous character, the study of the dynamics of fronts is carried out in almost all branches of physics, chemistry, fluid dynamics, populations dynamics. When described by reaction-diffusion equations, it often raises mathematical questions that turn out to be at the leading edge of nonlinear analysis. Fuelled by the number of potential applications, the amount of work on reaction-diffusion problems is enormous. The international competition is intense, and the subject attracts the attention of some of the best experts in mathematical analysis and nonlinear partial differential equations. The members of the proposing teams are themselves at the leading edge, and several recent advances in the understanding of reaction-diffusion front propagation are due to them: new notions of propagation, construction and classification of multi-dimensional waves, discovery of new estimates. We want in this proposal to extend and further these ideas.