Stationary solutions for a boundary controlled Burgers' equation

Citation
A. Balogh et al., Stationary solutions for a boundary controlled Burgers' equation, MATH COMP M, 33(1-3), 2001, pp. 21-37
Citations number
19
Categorie Soggetti
Engineering Mathematics
Journal title
MATHEMATICAL AND COMPUTER MODELLING
ISSN journal
08957177 → ACNP
Volume
33
Issue
1-3
Year of publication
2001
Pages
21 - 37
Database
ISI
SICI code
0895-7177(200101/02)33:1-3<21:SSFABC>2.0.ZU;2-I
Abstract
This paper is concerned with the stationary solutions of a one-parameter fa mily of boundary control problems for a forced Viscous Burgers' equation. W e assume that the forcing term possesses a special symmetry that greatly ai ds in our analysis. The parameter characterizing the family enters as a sca lar gain in a proportional error boundary feedback control scheme. We show that as the gain varies from zero to infinity, the stationary solutions und ergo an interesting bifurcation. Namely, when the gain is zero, there are i nfinitely many stationary solutions, the one-dimensional subspace of all co nstants. When the gain is positive, the constants are no longer solutions. For small positive values of the gain, there are three distinct nonconstant stationary solutions, and for sufficiently large values of the gain there is a single, asymptotically stable equilibrium. (C) 2001 Elsevier Science L td. All rights reserved.