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Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations

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López Montes, Antonio and Zhang, Xu and Zuazua Iriondo, Enrique (2000) Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations. Journal de Mathématiques Pures et Appliquées, 79 (8). pp. 741-808. ISSN 0021-7824

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021782499001440


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Abstract

In this paper we prove that the null controllability property of the heat equation may be obtained as limit of the exact controllability properties of singularly perturbed damped wave equations, We impose Dirichlet, homogeneous boundary conditions. The control is supported in a neighborhood of a subset of the boundary that satisfies the classical requirements to apply multiplier techniques. The proof needs an iterative argument that allows to treat separately the low and high frequencies and to make use of the dissipativity of the systems under consideration. This is combined with sharp observability estimates on the eigenfunctions of the Laplacian due to G. Lebeau and L. Robbiano, and global Carleman estimates


Item Type:Article
Uncontrolled Keywords:null controllability; heat equation; dissipative wave equation; global Carleman estimates
Subjects:Sciences > Physics > Mathematical physics
ID Code:21513
Deposited On:23 May 2013 10:43
Last Modified:12 Dec 2018 15:07

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