| Title:
|
$H^2$ convergence of solutions of a biharmonic problem on a truncated convex sector near the angle $\pi $ (English) |
| Author:
|
Tami, Abdelkader |
| Author:
|
Tlemcani, Mounir |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
383-395 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a biharmonic problem $\Delta ^{2}u_{\omega }=f_\omega $ with Navier type boundary conditions $u_{\omega }=\Delta u_{\omega }=0$, on a family of truncated sectors $\Omega _{\omega }$ in $\mathbb {R}^2$ of radius $r$, $0<r<1$ and opening angle $\omega $, $\omega \in (2\pi /3,\pi ]$ when $\omega $ is close to $\pi $. The family of right-hand sides $(f_\omega )_{\omega \in (2\pi /3,\pi ]}$ is assumed to depend smoothly on $\omega $ in $L^{2}(\Omega _{\omega })$. The main result is that $u_{\omega }$ converges to $u_\pi $ when $ \omega \rightarrow \pi $ with respect to the $H^2$-norm. We can also show that the $H^2$-topology is optimal for such a convergence result. (English) |
| Keyword:
|
sector |
| Keyword:
|
convex |
| Keyword:
|
biharmonic |
| Keyword:
|
elliptic |
| Keyword:
|
singularity |
| Keyword:
|
convergence |
| Keyword:
|
Sobolev space |
| MSC:
|
35B40 |
| MSC:
|
35B45 |
| MSC:
|
35J25 |
| MSC:
|
35J40 |
| MSC:
|
35J75 |
| MSC:
|
35Q99 |
| idZBL:
|
07361061 |
| idMR:
|
MR4263157 |
| DOI:
|
10.21136/AM.2021.0284-19 |
| . |
| Date available:
|
2021-05-20T13:34:42Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148900 |
| . |
| Reference:
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