Analyzing the dynamics of the forced Burgers equation. (2000)

• Record Type: Journal Article
• Authors: Smaoui, Nejib
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 3(2000)
• Page Start: 269
• Page End: 285
• Publication Date: 2000
• Subjects: parabolic equation -- reaction-diffusion equations -- inertial manifold -- Kwak transformation; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000241
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation ( u t + u u x − v u x x = F ) . A nonlinear transformation introduced by Kwak is used to embed the scalar Burgers equation into a system of reaction diffusion equations. The Kwak transformation is used to determine the existence of an inertial manifold for the 2-D Navier-Stokes equation. We show analytically as well as numerically that the two systems have a similar, long-time dynamical, behavior for large viscosity v .