| Language |
English
|
| From |
2010/11/16 15:30
|
| To |
2010/11/16 17:30
|
| Place | Room 552, Building No.3, Faculty of Science, Kyoto University |
| Seminar Name | NLPDE Seminar |
| Title |
Transversality of stable and Nehari manifolds for a semilinear heat equation |
| Field |
Analysis
|
| Speakers | Noriko Mizoguchi |
| Affiliation | Tokyo Gakugei University |
| Note | It is well known that for the subcritical semilinear heat equation,
negative initial energy is a sufficient condition for finite time blowup of the solution.
We show that this is no longer true when the energy functional is replaced with the Nehari functional,
thus answering negatively a question left open by Gazzola and Weth (2005).
Our proof proceeds by showing that the local stable manifold of any non-zero steady state solution
intersects the Nehari manifold transversally.
As a consequence, there exist solutions converging to any given steady state,
with initial Nehari energy either negative or positive. (This is a joint work with F. Dickstein, Ph. Souplet and F. Weissler.) |
|