| Title:
|
$L^\infty$ estimates of solution for $m$-Laplacian parabolic equation with a nonlocal term (English) |
| Author:
|
Hou, Pulun |
| Author:
|
Chen, Caisheng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
389-400 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we consider the global existence, uniqueness and $L^{\infty }$ estimates of weak solutions to quasilinear parabolic equation of $m$-Laplacian type $u_{t}-\mathop {\rm div}(|\nabla u|^{m-2}\nabla u)=u|u|^{\beta -1}\int _{\Omega } |u|^{\alpha } {\rm d} x$ in $\Omega \times (0,\infty )$ with zero Dirichlet boundary condition in $\partial \Omega $. Further, we obtain the $L^{\infty }$ estimate of the solution $u(t)$ and $\nabla u(t)$ for $t>0$ with the initial data $u_0\in L^q(\Omega )$ $(q>1)$, and the case $\alpha +\beta < m-1$. (English) |
| Keyword:
|
$m$-Laplacian parabolic equations |
| Keyword:
|
global existence |
| Keyword:
|
uniqueness |
| Keyword:
|
$L^{\infty }$ estimates |
| MSC:
|
35A01 |
| MSC:
|
35A02 |
| MSC:
|
35B45 |
| MSC:
|
35D30 |
| MSC:
|
35K20 |
| MSC:
|
35K65 |
| MSC:
|
35K92 |
| idZBL:
|
Zbl 1249.35177 |
| idMR:
|
MR2905412 |
| DOI:
|
10.1007/s10587-011-0083-1 |
| . |
| Date available:
|
2011-06-06T10:30:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141542 |
| . |
| Reference:
|
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