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Digitale Medien

Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms (1999)

Fernández, L. A. ; Zuazua, E.

Springer

Journal of optimization theory and applications 101 (1999), S. 307-328

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ISSN: 1573-2878

Schlagwort(e): Approximate controllability ; exact finite-dimensional controllability ; semilinear heat equation ; optimal control

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1021737526541

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