Full paper in PDF:
$%M. Kirane and M. Qafsaoui, On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form, Rev. Mat. Complut. 15 (2002), no. 2, 585598.%$

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
Université d’Orléans — I.U.T. d’Orléans
Rue d’Issoudun, B.P. 6729
45067 Orléans cedex 2 — France

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.