| Univ. Tokyo | Math. Sci. | FMSP |

Date: July 25 - 26, 2013
Place: Room 002, Graduate School of Mathematical Sciences, the University of Tokyo
1. Henri Berestycki (EHESS)
Theme: Nonlinear diffusion equations in inhomogeneous media
2. Frank Merle (Univ. Cergy Pontoise / IHES)
Theme: Solitons in dispersive equations and their asymptotic behavior
10:30-12:00 (Lunch) 13:30-15:0015:20-16:50
July 25 Berestycki - Berestycki Merle
July 26 Berestycki - Merle Merle

1. Henri Berestycki: "Reaction-diffusion equations in non homogeneous media"

Abstract: In this series of lectures, I will discuss some nonlinear partial differential equations of elliptic or parabolic types that are spatially inhomogeneous. The motivation comes mostly from ecology, but such models also arise in biology and medicine. Some recent progress has been achieved with new ideas that I will present in the mini-course.
Topics include waves guided by the medium, propagation involving fast diffusion on a line, propagation and spreading speeds in non-homogeneous media and a model for the effect of climate change on biological populations.

2. Frank Merle: "Soliton and asymptotic behavior for dispersive PDE"

Abstract: I will present recent works on critical problems including the energy critical nonlinear wave and the mass critical generalized KdV equation. The goal is to understand the qualitative behavior of a general solution asymptotically in time (for large time for global in time solution and if not close to the blow-up time ).
These descriptions in particular involve solitons. The methods for obtaining these results include Rigidity or Liouville theorems, dynamical system, soliton resolution conjecture, Minimal Element for dispersive equation, Kenig-Merle method for critical problem.

Organizer: Hiroshi Matano, E-mail: matanoms.u-tokyo.ac.jp
Access map: http://www.ms.u-tokyo.ac.jp/access_e/index_e.html
Leading Graduate Course for Frontiers of Mathematical Sciences and Physics,
The University of Tokyo