Abstract
The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, priori estimates for the solution was given. At last, the existence of the weak solution of MKdV-Burgers equation was proved and the global-exponential and asymptotic stability of the solution of MKdV-Burgers equation was given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Russell D L and Zhang B Y. Exact controllability and stabilizability of the Korteweg-de Vries equation[J]. Trans Amer Math, 1996, 348(9): 3643–3672.
Naumkin P I and Shishmarev I A. On the decay of step-like data for the Korteweg-de-Vries-Burgers equation[J]. Funktsional Anal Prilozhen, 1992, 26(2), 88–93.
Liu Weijiu and Miroslav Krstic. Global boundary stabilization of the Korteweg-de Vries Burgers equation[J]. Computational and Applied Mathematics, 2002, 21(1), 315–354.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (No.10071033) and the Natural Science Foundation of Jiangsu Province (No.BK2002003)
Rights and permissions
About this article
Cite this article
Tian, Lx., Zhao, Zf. & Wang, Jf. Boundary control of MKdV-Burgers equation. Appl Math Mech 27, 109–116 (2006). https://doi.org/10.1007/s10483-006-0114-z
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-0114-z