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

Objectives

The aim of this workshop is to foster the interaction in the different groups of mathematicians who either study or apply nonlinear diffusion equations in their work: these include mathematicians specialized in partial differential equations, geometric analysis, and the calculus of variations, and, in terms of fields of applications, people studying kinetic theory, fluid mechanics, thin films, probabilistic approaches of particle systems, plasma and solid state physics, and exotic materials.

While recent conferences devoted to optimal transportation techniques and kinetic theory have often touched different aspects of nonlinear diffusions, not a single conference has chosen this question as its overarching theme. Nor have many succeeded in bridging the gap between geometers working on curvature flows and applied mathematicians studying fluids, thin films, and kinetic theory. This time is the right one for a workshop to showcase recent progresses and highlight the challenges, setting the stage for future developments, new collaborations, and cross-pollination between different communities. Since more and more young researchers are getting involved in this area, it is expected that the workshop will play a structuring role in the development of the field.

A number of the proposed participants have already expressed their interest in the possibility of participating in a conference devoted to entropies and nonlinear diffusions. There is also a large interest among young researchers as can be seen from the success of recent summer schools in which some of the recent developments have been disseminated: CIME summer school ''Optimal transportation and applications'' (Martina Franca, Italy, 2000), UIMP-RSME summer school ''Recent Trends in Partial Differential Equations'' (Santander, Spain, 2004).