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Null controllability of the 1-d heat equation as limit of the controllability of dissipative wave equations

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López Montes, Antonio and Zuazua Iriondo, Enrique (1998) Null controllability of the 1-d heat equation as limit of the controllability of dissipative wave equations. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 327 (8). pp. 753-758. ISSN 0764-4442

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Official URL: http://www.sciencedirect.com/science/article/pii/S076444429880164X


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Abstract

We consider the 1 - d wave equation epsilon u(tt) - u(tt) + u(t) = 0 With Dirichlet boundary conditions in a bounded interval. It is well known that for any epsilon > 0 this system is exactly controllable, with controls distributed on some open subinterval. It is also well known that the heat equation u(t) - u(xx) = 0 is null controllable. In this Note we prove that the null controls for the dissipative wave equations can be built so that they converge to a null control for the heat equation as epsilon --> 0. This shows the continuity of the null controls with respect to the singular perturbation under consideration


Item Type:Article
Uncontrolled Keywords:Controllability; Heat equation; Nonlinear programming
Subjects:Sciences > Physics > Mathematical physics
Sciences > Mathematics > Differential equations
ID Code:21517
Deposited On:23 May 2013 11:01
Last Modified:12 Dec 2018 15:08

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