| 発表言語 |
英語
|
| 開催日 |
2010年11月16日 15時30分
|
| 終了日 |
2010年11月16日 17時30分
|
| 開催場所 | 京都大学理学部3号館 (数学教室) 552号室 |
| セミナー名 | NLPDEセミナー |
| タイトル |
Transversality of stable and Nehari manifolds for a semilinear heat equation |
| 分野 |
解析
|
| 講演者名 | Noriko Mizoguchi |
| 講演者所属 | Tokyo Gakugei University |
| 備考 | 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.) |
|