Burgers' equation with nonlinear boundary feedback: H-1 stability, well-posedness and simulation

Citation
A. Balogh et M. Krstic, Burgers' equation with nonlinear boundary feedback: H-1 stability, well-posedness and simulation, MATH PROB E, 6(2-3), 2000, pp. 189-200
Citations number
12
Categorie Soggetti
Engineering Mathematics
Journal title
MATHEMATICAL PROBLEMS IN ENGINEERING
ISSN journal
1024123X → ACNP
Volume
6
Issue
2-3
Year of publication
2000
Pages
189 - 200
Database
ISI
SICI code
1024-123X(2000)6:2-3<189:BEWNBF>2.0.ZU;2-K
Abstract
We consider the viscous Burgers' equation under recently proposed nonlinear boundary conditions and show that it guarantees global asymptotic stabiliz ation and semiglobal exponential stabilization in H-1 sense. Our result is global in time and allows arbitrary size of initial data. It strengthens re cent results by Byrnes, Gilliam, and Shubov, Ly, Mease, and Titi, and Ito a nd Yan. The global existence and uniqueness of classical solutions follows from the general theory of quasi-linear parabolic equations. We include a n umerical result which illustrates the performance of the boundary controlle r.