Nonlinear diffusions: entropies, asymptotic behavior and applications (06w5039)


Eric Carlen (Rutgers University)

(Imperial College, London, GB)

(Université Paris-Dauphine)


Robert McCann (University of Toronto)


Scientists have long recognized the importance of diffusion in modelling everything from the spread of pollutants to the stock market. If feedback mechanisms are present in the system, then the rates of the process may vary from point to point depending on the gradient and concentration of the material diffusing. The system can then exhibit dramatic transitions, nonlinear behaviour, and pattern formation which challenge prediction and analysis. Such models are used in the manufacture of semiconductors, oil recovery, and the assessments of environmental impact.

Next week (April 15 - 20, 2006) a group of leading mathematicians and scientists will converge on the Banff International Research Station to exchange news of the latest discoveries concerning these phenomena, collaborate on vexing problems, and chart the course of research for the upcoming years. Results obtained using different methodologies --- theoretical analysis, computer simulations, laboratory experiments --- will be compared and integrated into an overarching understanding of nonlinear diffusion. The event is co-organized by a team of scientists representing Canada, the US and Europe: Eric Carlen (Atlanta), Jose Antonio Carrillo (Barcelona), Jean Dolbeault (Paris), Peter Markowich (Vienna) and Robert McCann (Toronto).

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is administered by the Pacific Institute for the Mathematical Sciences, which itself is a collaborative venture between the major universities in Alberta, BC and Washington State.