Controlling the dynamics of Burgers equation with a high-order nonlinearity

Nejib Smaoui

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-12

Abstract:

We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e., u t = ν u x x − u n u x + m u + h ( x ) ). We show existence of an absorbing ball in L 2 [ 0 , 1 ] and uniqueness of steady state solutions for all integer n ≥ 1 . Then, we use an adaptive nonlinear boundary controller to show that it guarantees global asymptotic stability in time and convergence of the solution to the trivial solution. Numerical results using Chebychev collocation method with backward Euler time stepping scheme are presented for both the controlled and the uncontrolled equations illustrating the performance of the controller and supporting the analytical results.

Date: 2004
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2004/230358.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2004/230358.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:230358

DOI: 10.1155/S0161171204404116

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().