CIMPA Lecturer 1: Dr. Doina Cioranescu

CIMPA-IMAMIS-Philippines School on Numerical Methods for Partial Differential Equations
27 August - 7 September 2007
Ateneo de Manila University, Quezon City, Philippines
Hosted by: Mathematics Department, Ateneo de Manila University

Lecturer: Doina Cioranescu, Ph.D.
Affiliation: Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie Paris 6, Paris, France
E-mail: cioran@ann.jussieu.fr

Topic: Advanced Partial Differential Equations

Outline:

1. Distributions and equations with constant coefficients·

• General notions about distributions
• Elliptic operators
• Local solvability of constant coefficients PDE

2. Sobolev spaces· Introduction· Imbedding and trace theorems· Generalized solutions

3. Elliptic equations and boundary-value problems

• Laplace and Poisson equations· Maximum principles
• Variational formulation, Lax-Milgram theorem
• Dirichlet, Neumann and Robin problems
  

4. The heat equation

• Variational formulation
• Existence and uniqueness theorems
  

5. The wave equation

• Variational formulation
• Existence and uniqueness theorems
  

6. Navier-Stokes equation

• Variational formulation
• Existence and uniqueness theorems
  

Schedule:

August 27, 10:00 a.m. - 12:00 noon, Rm. SOM 111
August 28, 9:00 - 11:00 a.m., Rm. SOM 111
September 4, 3:00 - 5:00 p.m., Rm. SOM 111

Raffy
The Pisay '77 Blogger
8/28/07