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 Nefedov, Nikolai, Lomonosov Moscow State University, Russia Asymptotic method of differential inequalities for nonlinear singularly perturbed PDE’s with internal layers New asymptotic method of investigation of singularly perturbed equations which was recently developed by the author is presented. This approach is based on constructing of upper and lower solutions by using formal asymptotics. The method is applied to some singularly perturbed problems which have solutions with internal layers: the parabolic problems with periodic solutions, the elliptic systems with fast and slow equations with internal layers and in the case of exchahge of stability, integro-differential equations. The existence, asymptotic behaviour and stability of the solutions are stated by the developed method. This work is supported by RFFI, pr. N 98-01-00916.