|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Instability of Steady States for nonlinear parabolic and damped hyperbolic equations | | Stephen Pankavich
; Petronela Radu
; | | Date: |
28 Oct 2011 | | Abstract: | We consider steady solutions of semi-linear hyperbolic and parabolic
equations of the form $partial_{tt}u + a(t) partial_t u + Lu = f(x, u)$ and
$a(t) partial_t u + Lu = f(x, u)$ with a damping coefficient $a(t)$ that is
possibly sign-changing and determine precise conditions for which linear
instability implies nonlinear instability. More specifically, we prove that
linear instability with a positive eigenfunction gives rise to nonlinear
instability by either exponential growth or finite-time blow-up. We then
discuss a few examples to which our main theorem is immediately applicable,
including equations with supercritical and exponential nonlinearities. | | Source: | arXiv, 1110.6240 | | 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