2019
DOI: 10.1016/j.jde.2018.08.046
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Controllability of a 4 × 4 quadratic reaction–diffusion system

Abstract: We consider a 4 × 4 nonlinear reaction-diffusion system posed on a smooth domain Ω of R N (N ≥ 1) with controls localized in some arbitrary nonempty open subset ω of the domain Ω. This system is a model for the evolution of concentrations in reversible chemical reactions. We prove the local exact controllability to stationary constant solutions of the underlying reaction-diffusion system for every N ≥ 1 in any time T > 0. A specificity of this control system is the existence of some invariant quantities in the… Show more

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Cited by 10 publications
(11 citation statements)
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References 45 publications
(103 reference statements)
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“…. By using the return method, the author proves the local null-controllability around (0, u * 2 , 0, 0) of (40) (see [28]). More precisely, for this system, a reference trajectory is not difficult to construct.…”
Section: The Inverse Mapping Theorem In Appropriate Spacesmentioning
confidence: 98%
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“…. By using the return method, the author proves the local null-controllability around (0, u * 2 , 0, 0) of (40) (see [28]). More precisely, for this system, a reference trajectory is not difficult to construct.…”
Section: The Inverse Mapping Theorem In Appropriate Spacesmentioning
confidence: 98%
“…Another strategy to get local controllability result for (NL), called the Small L ∞perturbations method is used in [1], [4], [28], [31] and [38]. This method requires the null-controllability of a family of linear parabolic systems.…”
Section: 2mentioning
confidence: 99%
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“…The proof of Theorem 1.3 is a consequence of the (global) null-controllability of the linear heat equation with a bounded potential (due to Andrei Fursikov and Oleg Imanuvilov, see [23] or [21, Theorem 1.5]) and the small L ∞ perturbations method (see [3, Lemma 6] and [1], [5], [30], [33], [40] for other results in this direction).…”
Section: Contentsmentioning
confidence: 99%