صندلی اداری

EXPLICIT DECAY BOUNDS IN SOME QUASI-LINEAR N-DIMENSIONAL PARABOLIC PROBLEMS

L. Ragoub

Abstract


The investigation made in this paper is to derive two new maximumprinciples for two different parabolic equations of the form$a(t)f(u)g(|{\bf{\nabla}}\,u|^{2})\Delta\,u=u_{t}$ and$a(t)f(u)(G(u))_{,kk}=u_{t}$, where $u_{t}:=\frac{\partialu}{\partial t}$, $x\in\Omega,\,\,t>0$ and $\Omega$ is a boundeddomain of $\RR^{N}$, $N\,\geq\,2$.As an application of this derivation, we obtain explicit decaybounds for $u$ and its gradient $|{\bf{\nabla}}\,u|$ under theDirichlet boundary condition. The main tools of this investigationare the maximum principles of Hopf, Nirenberg and Friedman.

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