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Smaoui, Nejib; El-Kadri, Alaa; Zribi, Mohamed

Nonlinear boundary control of the unforced generalized Korteweg-de Vries-Burgers equation. (English) Zbl 1194.35389

Nonlinear Dyn. 60, No. 4, 561-574 (2010).
Summary: We consider the boundary control problem of the unforced generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is [0,1]. Three control laws are derived for this equation and the \(L^{2}\)-global exponential stability of the solution is proved analytically. Numerical results using the finite element method (FEM) are presented to illustrate the developed control schemes.

Cited in 10 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B35 Stability in context of PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Keywords:

unforced generalized Korteweg-de Vries-Burgers equation; boundary control; global stability
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References:

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