Asymptotic behaviour of solutions of some nonlinear parabolic or elliptic equations

Article type: Research Article

Authors: Kondratiev, V.A. | Véron, L.^;

Affiliations: Faculty of Mathematics and Mechanics, Lomonossov University, Moscow, Russia | Laboratoire de Mathématiques et Physique Théoretique, CNRS UPRES-A 6083, Faculté des Sciences et Techniques, Université François Rabelais, Parc de Grandmont, 37200 Tours, France

Note: [] Corresponding author. E-mail: veronl@univ-tours.fr.

Abstract: We study the asymptotic behaviour of the solutions of the parabolic equation (1) ∂u/∂t−Lu+a(x)|u|q−1u=0 or the elliptic equation (2) ∂2u/∂t2+Lu−a(x)|u|q−1u=0 in Ω×(0,∞) when Ω is bounded, u satisfies the Neumann boundary condition in ∂Ω×(0,∞),L is a linear strongly elliptic operator in Ω,q is bigger than 1 and a(x)≥0. We also study the vanishing property of t$\mapsto $u(x,t) when 0 < q < 1.

DOI: 10.3233/ASY-1997-14202

Journal: Asymptotic Analysis, vol. 14, no. 2, pp. 117-156, 1997