ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Goritsky, Andrey Yu., Moscow State University, Russia. Integral manifolds with exponential tracking. Equation du/dt + Au = F (u, t) in a Hilbert space is studied. Here A is a linear operator semibounded below and F (u, t) satisfies the global Lipschitz condition with respect to u. If the spectral gap property holds there exist integral manifolds M_{±} that exponentially attract any solution u(t) when t → ±∞. The manifold M_{+} is invariant and finite dimensional, M_{−} has a finite codimension. Studying the behavior of solutions u(t) when t → +∞ we suggest an explicit construction of finite dimensional semiinvariant integral manifold with exponential tracking. Results are obtained jointly with V. V. Chepyzhov. Reference: V. V. Chepyzhov, and A. Yu. Goritsky, Global integral manifolds with exponential tracking for nonautonomous equations, Russ. Jour. Math. Phys. 5(1), 1997, 9-28