Equations aux dérivées partielles

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.