Exact controllability of semilinear plate equations
By Xu Zhang. Asymptotic Analysis, 2001
48 citations recorded by the source corpus.
In this paper, we obtain the exact controllability for a class of semilinear plate equations under a superlinear growth assumption on the nonlinearity. For this purpose, we need an explicit observability estimate for the linear plate equation with a potential, which is derived by means of Carleman estimates together with the usual energy estimate.
Subfields: Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/8a9f23c6d0eac4962ebe1411923abd6158b09c31
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In Control and Systems Engineering
- Xiaoyu Fu
- Xu Zhang
- Irena Lasiecka
- X. Zhang
- Roberto Triggiani
- Igor D. Chueshov
- Enrique Zuazua
- Mark R. Opmeer
In Numerical Analysis
Citations in the corpus
- On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials (2008, unknown): “We refer to [31], [28] and [21] for a discussion of observability estimates for these models.”
- A weighted identity for partial differential operators of second order and its applications (2006, methodology): “Aussi, ceci amène les résultats de contrôlabilité/observabilité pour les équations des plaques dans [8] et les résultats pour le problème inverse des équations de Schrödinger dans [1].”
- Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carleman estimates. Part I: H 1(Ω)-estimates (2004, background): “Moreover, an explicit constant in the continuous observability inequality is useful in at least two contexts: (i) in the corresponding semilinear problems [16], [50], and (ii) in yielding the minimal norm among the steering controls [43, Appendix; 13, Appendix].”
- A unified controllability/observability theory for some stochastic and deterministic partial differential equations (2010, background): “2, one can deduce the controllability/observability for the Schrödinger equation and plate equation appeared in [23] and [48], respectively.”