|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
18 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Large-time rescaling behaviors for large data to the Hele-Shaw problem | | Yulin Lin
; | | Date: |
16 Oct 2008 | | Abstract: | This paper addresses a rescaling behavior of some classes of global solutions
to the zero surface tension Hele-Shaw problem with injection at the origin,
${Omega(t)}_{tgeq 0}$. Here $Omega(0)$ is a small perturbation of
$f(B_{1}(0),0)$ if $f(xi,t)$ is a global strong polynomial solution to the
Polubarinova-Galin equation with injection at the origin and we prove the
solution $Omega(t)$ is global as well. We rescale the domain $Omega(t)$ so
that the new domain $Omega^{’}(t)$ always has area $pi$ and we consider
$partialOmega^{’}(t)$ as the radial perturbation of the unit circle centered
at the origin for $t$ large enough. It is shown that the radial perturbation
decays algebraically as $t^{-lambda}$. This decay also implies that the
curvature of $partialOmega^{’}(t)$ decays to 1 algebraically as
$t^{-lambda}$. The decay is faster if the low Richardson moments vanish. We
also explain this work as the generalization of Vondenhoff’s work which deals
with the case that $f(xi,t)=a_{1}(t)xi$. | | Source: | arXiv, 0810.2975 | | 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 claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER