ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34-35 Boucherif, Abdelkader, University of Tlemcen, Algeria A free boundary problem for a reaction-diffusion equation Certain phase-change processes, such as the one-dimensional Stephan problem, are described by the following free boundary value problem:

−(k(x, y)Ψ(y′))′ = f(x, y, y′) x > s y(s)  = A y(x)  = B for x = +∞ k(s, y(s))Ψ(y′(s)) = +∅(s) .

where s is a priori unknown and has to be determined as part of the solution to the problem. Existence and uniqueness results are presented. This is based on a joint work with Y. Benkamra