- Series
- PDE Seminar
- Time
- Tuesday, August 31, 2010 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 114
- Speaker
- Professor Tai-Peng Tsai – Department of Mathematics, University of British Columbia – ttsai@math.ubc.ca – http://www.math.ubc.ca/~ttsai/
- Organizer
- Ronghua Pan
Consider a nonlinear Schrodinger
equation in $R^3$
whose linear part has three or more eigenvalues
satisfying some resonance
conditions. Solutions which are initially small in
$H^1 \cap
L^1(R^3)$ and inside a neighborhood of the first excited state
family are shown to converge to either a first excited state or a
ground state at time infinity. An essential part of our analysis
is on the linear and nonlinear estimates near nonlinear excited
states, around which the linearized operators have eigenvalues
with nonzero real parts and their corresponding eigenfunctions
are
not uniformly localized in space. This is a joint work with Kenji Nakanishi
and Tuoc Van Phan.The preprint of the talk is available at
http://arxiv.org/abs/1008.3581