- Series
- CDSNS Colloquium
- Time
- Monday, August 31, 2015 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Jiayin Jin – Georgia Inst. of Technology
- Organizer
- Rafael de la Llave
We
construct invariant manifolds of interior multi-spike states for the
nonlinear Cahn-Hilliard equation and then investigate the dynamics on
it. An equation for the motion of the spikes is derived. It turns out
that the dynamics of interior spikes has a global character and each
spike interacts with all the others and with the boundary. Moreover, we
show that the speed of the interior spikes is super slow, which
indicates the long time existence of dynamical multi-spike solutions in
both positive and negative time. This result is obtained through the
application of a companion abstract result concerning the existence of
truly invariant manifolds with boundary when one has only approximately
invariant manifolds.