|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Dispersive limit from the Kawahara to the KdV equation | | Luc Molinet
; Yuzhao Wang
; | | Date: |
3 May 2012 | | Abstract: | We investigate the limit behavior of the solutions to the Kawahara equation
$$ u_t +u_{3x} +varepsilon u_{5x} + u u_x =0, $$ as $ 0<varepsilon o 0 $.
In this equation, the terms $ u_{3x} $ and $ varepsilon u_{5x} $ do compete
together and do cancel each other at frequencies of order $
1/sqrt{varepsilon} $. This prohibits the use of a standard dispersive
approach for this problem. Nervertheless, by combining different dispersive
approaches according to the range of spaces frequencies, we succeed in proving
that the solutions to this equation converges in $ C([0,T];H^1(R)) $ towards
the solutions of the KdV equation for any fixed $ T>0$. | | Source: | arXiv, 1205.0729 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER