RMC - Vol. 15, Num. 2 - M. Kirane/M. Qafsaoui

Full paper in PDF:
$%M. Kirane and M. Qafsaoui, On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form, Rev. Mat. Complut. 15 (2002), no. 2, 585–598.%$

On the Asymptotic Behavior for Convection-Diffusion Equations Associated to Higher Order Elliptic Operators in Divergence Form

Mokhtar KIRANE and Mahmoud QAFSAOUI

Laboratoire de Mathématiques Université de la Rochelle Pôle Sciences et Technologies Avenue Michel Crépeau 17042 La Rochelle cedex — France mokhtar.kirane@univ-lr.fr	Université d’Orléans — I.U.T. d’Orléans Rue d’Issoudun, B.P. 6729 45067 Orléans cedex 2 — France Mahmoud.Qafsaoui@iut.univ-orleans.fr

Received: November 2, 2000
Revised: February 27, 2002

ABSTRACT

We consider the linear convection-diffusion equation associated to higher order elliptic operators

(1)

{ ut+Ltu = a \~/ u on Rn × (0, oo ) u(0)= u0 (- L1(Rn),

where $a$ is a constant vector in $n R$ , $* m (- N$ , $n> 1$ and $L0$ belongs to a class of higher order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on $n R$ . The aim of this paper is to study the asymptotic behavior, in $p L$ ( $1< p< oo$ ), of the derivatives $g D u(t)$ of the solution of (1) when $t$ tends to $oo$ .

2000 Mathematics Subject Classification: 35B40, 35K25, 35K57, 35G05, 35A08.