What is the common point between the development of a migrain, crime evolution in a town, the invasion of a piece of land by a pest or the propagation of a fire? They may all be described by reaction-diffusion processes. Trying to understand, or to describe, or to find possible common features to these events, lead us to the study of front propagation under reaction-diffusion processes.
One of the challenges in all the above processes is that they occur in highly heterogeneus media. The goal of this project is to make a leap forward in the description of front propagation with highly heterogeneous diffusion and transport processes. Mathematically, this will lead us to use elements from - and possibly to prove new results in - partial differential equations, infinite dimensional dynamical systems, nonlocal equations and nonlocal diffusion processes, nonlocal free boundary problems, nonstandard spatial couplings.
By the way, the images that you can see on this page and on the welcome page display the propagation of a front directed by a horizontal line with abnormally fast diffusion - here, the bottom line - The model that we use is relevant to describe various biological invasions driven by transportation networks - pine processionary moth, tiger mosquito... Numerical simulations due to A.-C. Coulon.
One of the challenges in all the above processes is that they occur in highly heterogeneus media. The goal of this project is to make a leap forward in the description of front propagation with highly heterogeneous diffusion and transport processes. Mathematically, this will lead us to use elements from - and possibly to prove new results in - partial differential equations, infinite dimensional dynamical systems, nonlocal equations and nonlocal diffusion processes, nonlocal free boundary problems, nonstandard spatial couplings.
By the way, the images that you can see on this page and on the welcome page display the propagation of a front directed by a horizontal line with abnormally fast diffusion - here, the bottom line - The model that we use is relevant to describe various biological invasions driven by transportation networks - pine processionary moth, tiger mosquito... Numerical simulations due to A.-C. Coulon.