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On a Constrained Approximate Controllability Problem for the Heat Equation

Author

Listed:
  • J. H. Ortega

    (Universidad del Bío-Bío)

  • E. Zuazua

    (Universidad Complutense de Madrid)

Abstract

In this work, we study an approximate control problem for the heatequation, with a nonstandard but rather natural restriction on thesolution. It is well known that approximate controllability holds. On theother hand, the total mass of the solutions of the uncontrolled system isconstant in time. Therefore, it is natural to analyze whether approximatecontrollability holds supposing the total mass of the solution to be a givenconstant along the trajectory. Under this additional restriction,approximate controllability is not always true. For instance, this propertyfails when Ω is a ball. We prove that the system is genericallycontrollable; that is, given an open regular bounded domain Ω, thereexists an arbitrarily small smooth deformation u, such that the system isapproximately controllable in the new domain Ω+u underthis constraint. We reduce our control problem to a nonstandard uniquenessproblem. This uniqueness property is shown to hold generically with respectto the domain.

Suggested Citation

  • J. H. Ortega & E. Zuazua, 2001. "On a Constrained Approximate Controllability Problem for the Heat Equation," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 29-64, January.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:1:d:10.1023_a:1026409821088
    DOI: 10.1023/A:1026409821088
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    Cited by:

    1. Hsieh Hsih-chia & Hsieh Pei-gin, 2004. "A Generalized Theory of Monetary and Macroeconomics," Money Macro and Finance (MMF) Research Group Conference 2004 50, Money Macro and Finance Research Group.

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