Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms

L. A. Fernández and E. Zuazua
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L. A. Fernández: Universidad de Cantabria
E. Zuazua: Universidad Complutense

Journal of Optimization Theory and Applications, 1999, vol. 101, issue 2, No 4, 307-328

Abstract: Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces.

Keywords: Approximate controllability; exact finite-dimensional controllability; semilinear heat equation; optimal control (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1021737526541

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