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 Date: July 25 - 26, 2013
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Place: Room 002, Graduate School of Mathematical Sciences, the University of Tokyo
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Lecturers:
1. Henri Berestycki (EHESS)
Theme: Nonlinear diffusion equations in inhomogeneous media
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2. Frank Merle (Univ. Cergy Pontoise / IHES)
Theme: Solitons in dispersive equations and their asymptotic behavior
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 PROGRAM:
| 10:30-12:00 | (Lunch) | 13:30-15:00 | 15:20-16:50
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| July 25 | Berestycki | - | Berestycki | Merle |
| July 26 | Berestycki | - | Merle | Merle |
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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.
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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.
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Organizer: Hiroshi Matano,
E-mail: matano ms.u-tokyo.ac.jp
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Access map: http://www.ms.u-tokyo.ac.jp/access_e/index_e.html
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