2018
DOI: 10.1016/j.jmaa.2017.12.031
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Controllability aspects of the Korteweg–de Vries Burgers equation on unbounded domains

Abstract: The aim of this work is to consider the controllability problem of the linear system associated to Korteweg-de Vries Burgers equation posed in the whole real line. We obtain a sort of exact controllability for solutions in L 2 loc (R 2 ) by deriving an internal observability inequality and a Global Carlemann estimate. Following the ideas contained in [26], the problem is reduced to prove an approximate theorem.2010 Mathematics Subject Classification. Primary: 35Q53, Secondary: 37K10, 93B05, 93D15.

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Cited by 5 publications
(4 citation statements)
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“…It shows that system (37) achieves the mean-square H ∞ performance under observer-based controller (6). Figure 5(B) demonstrates the mean-square H ∞ performance of the closed-loop system.…”
Section: Numerical Examples and Simulationmentioning
confidence: 93%
See 2 more Smart Citations
“…It shows that system (37) achieves the mean-square H ∞ performance under observer-based controller (6). Figure 5(B) demonstrates the mean-square H ∞ performance of the closed-loop system.…”
Section: Numerical Examples and Simulationmentioning
confidence: 93%
“…To prove the stability of the closed-loop system (8) or ( 9), it is sufficient to show the stability of the system (4), ( 5) subject to (6) or (7). Thus, we start with the stability analysis of the system (4), ( 5) subject to (6) or (7). The Lyapunov-Krasovskii functional (LKF) is selected for (4) and ( 5) as follows:…”
Section: Regional Stabilization Of Stochastic Kdvb Equationmentioning
confidence: 99%
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“…That is the reason that the Laplacian is added. From a mathematical point of view, there exist several results for the KdVB equation in both bounded and unbounded domains, concerning the global and local well-posedness problem [8], [26], [14] and [3]; the optimal control problem [4], [11]; the internal controllability problem on unbounded domain [17]; and the boundary feedback stabilization problem [23]. As far as we know, the internal controllability problem for (1) has not been studied and thus, our paper will fill this gap.…”
Section: Introductionmentioning
confidence: 99%