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oai:docta.ucm.es:20.500.14352/585042023-08-28T02:08:50Zcom_20.500.14352_14col_20.500.14352_15

López Montes, Antonio Zhang, Xu Zuazua Iriondo, Enrique 2023-06-20T18:44:55Z 2023-06-20T18:44:55Z 2000 0021-7824 10.1016/S0021-7824(99)00144-0 https://hdl.handle.net/20.500.14352/58504 http://www.sciencedirect.com/science/article/pii/S0021782499001440 http://www.sciencedirect.com/ 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 eng restricted access Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations journal article