$L^\infty$ estimates of solution for $m$-Laplacian parabolic equation with a nonlocal term

Title:

$L^\infty$ estimates of solution for $m$-Laplacian parabolic equation with a nonlocal term

Creator:

Hou, Pulun and Chen, Caisheng

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:40403d6f-2063-4ca0-8852-492c67a60232
uuid:40403d6f-2063-4ca0-8852-492c67a60232

Subject:

$m$-Laplacian parabolic equations, global existence, uniqueness, and $L^{\infty }$ estimates

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $\alpha +\beta < m-1$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

389-400

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:2

Harvested from:

CDK

Metadata only:

false