UCL - Differential equations

[INMA2345]

[30h + 22.5h] 5 credits

This course is taught in the 2d semester.

Teacher(s): Abdou Kouider Ben-Naoum, Jean Van Schaftingen

Language: French

Level: Second

Aims
Main themes
Content and teaching methods
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

This course treats boundary value problems for linear and nonlinear systems as well as periodical problems.

Main themes

Boundary value problems, periodical problems and some other topics selected by the students.

Content and teaching methods

Hilbert spaces, Lp spaces and Sobolev spaces ;
Notion of strong solutions and weak solutions of boundary value problems ;
Variational methods ;
Spectral methods ;
Bifurcation theory.

The students will have the opportunity to go deeper into a topic of their choice and to present it to their colleagues.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Prerequisite : INMA 1315 "Mathematical analysis : complements"

Course materials : some chapters of the following books :
- Critical Point Theory and Hamiltonian Systems, J. Mawhin et M. Willem, Applied Mathematical Society, 74 Springer Verlag ;
- Analyse convexe et problèmes variationnels, I. Ekeland et R. Temmam, Dunod Gauthier-Villars, 1994 ;
- A. K. Ben-Naoum et C. Finet, Analyse mathématique, Résumé de cours et exercices corrigés: Espaces de Lebesgue, Espaces de Hilbert et Distributions. De Boeck Université 1999.