1998 Burkina

1998 Burkina

Accueil
Remonter
1998 Burkina
CARI'98
1998 China
1998 Egypt
1998 Mauritania
1998 Vietnam

CIMPA-UNSA-UNESCO-BURKINA FASO SCHOOL

Evolution equations and applications

Objectives:

Introduce young researchers in mathematics to the main tools of analysis and numerical methods for solving, linear and nonlinear partial differential equations and their applications to models in physics.

Scientific committee and lecturers:

P. Benilan , Y. Cherruault, F. Conrad, J.I. Diaz, C. Goudjo, C. Lobry, A. Mignot, M.T. Niane, A. Ouedraogo, B. Somé, H. Touré

Scientific directors:

P. Bénilan (Besançon, France), Y. Cherruault (Paris VI, France), J.I. Diaz (Madrid, Espagne), A. Ouedraogo , B. Somé, H. Touré (Ouagadougou, Burkina Faso)

Working languages :

English and French.

Date and location:

July 13-31, 1998, Ouagadougou, Burkina Faso

Scientific program:

Week 1 : Hille-Yosida theory, analytic semigroup, maximal regularity. Numerical analysis of PDE: classical methods and finite volume method. Biomedical modelling, compartment analysis, optimal control and optimisation in biomedecine.

Week 2 : Accretive operators in Banach spaces, Crandall-Ligget theorem, convergence and approximation. Fundamental solutions of linear PDE, Cauchy problem, boundary value problem, classification of PDE. Nonlinear PDE, semilinear equations, quasilinear equations, inequations, degenerate problems, variational and fixed points methods. Control of linear systems in finite dimensional spaces ; exact controllability and approximate contrallability in infinite dimensional spaces.

Week 3 : Asymptotic behavior of evolution problems, Lyapunov functional, gradient like systems, attractors and convergence of solutions. Free boundary problems, blow up and shrinking in finite time; particular solutions (stationary, self similar, soliton), stability, ordered and symmetrisation methods. The principle and mathematical basis of G. Adomian method, application to PDE, convergence and comparison with classical methods.

Prerequisites :

Researcher in mathematics having started their thesis with a good training in at least one the following domain: functional analysis, differential equations, nonlinear analysis and numerical analysis.