MATH 4201: Partial differential equations
- Laplace equation: resolution of the equation -Laplacian(u)=f, in a bounded domain, using functional methods (variational formulation, Sobolev spaces, Lax-Milgram theorem), smoothness, maximum principle (weak and strong).
- Nonlinear reaction-diffusion equation:
existence of strong solutions in small time for d_t u - Laplacian(u)=f(u) where f is a smooth given function (approximation by Galerkin method, existence of a solution, regularity, blow up, positivity).
- Introduction to pseudo-differential operators: symbol, operator associated with a symbol, symbolic computation, inversion of an elliptic operator, notion of wavefront.
contacts
Responsable du MA1 :
François Brunault
ENS, site Monod, bâtiment GN1 (l’arche), 4e étage
Gestionnaires de scolarité
École normale supérieure
Sophie Bonche
Site Monod, bâtiment LE (accolé au GN1, côté nord de l’allée d’Italie)
bureau 536, allée Allan C. Wilson
04.72.72.85.53
Université Claude Bernard
Aline Ghedira et Ségolène Serre
scolarite.mathematiques@univ-lyon1.fr
ENS de Lyon
15 parvis René Descartes - BP 7000
69342 Lyon Cedex 07 - FRANCE
Tél. : Site René Descartes (siège) : +33 (0) 4 37 37 60 00
Site Jacques Monod : +33 (0) 4 72 72 80 00