|Location:||MSRI: Simons Auditorium|
For any hyperbolic systems (the hyperbolic systems we mean here are systems
that the sepctra of the linear operator of these systems are not the pure imaginary), if
the inhomogeneous terms decrease exponentially about time t in and small, the linear
perturbations are small and the higher order perturbations are bounded, our main result
(Theorem 2.1) shows that there is a small solution that decreases exponentially in .
We take the time-dependent complex Ginaburg-andau equations, Boussinesq equations
and the duffing equations, which are infinite-dimensional and finite-dimensional systems
respectively, as examples.