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Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms

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  • V. R. Cabanillas
  • S. B. de Menezes
  • E. Zuazua

Abstract

We consider the null controllability problem for the semilinear heat equation with nonlinearities involving gradient terms in an unbounded domain Ω of ℝ N with Dirichlet boundary conditions. The control is assumed to be distributed along a subdomain ω such that the uncontrolled region Ω\ω is bounded. Using Carleman inequalities, we prove first the null controllability of the linearized equation. Then, by a fixed-point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is C1 and globally Lipschitz, the system is null controllable.

Suggested Citation

  • V. R. Cabanillas & S. B. de Menezes & E. Zuazua, 2001. "Null Controllability in Unbounded Domains for the Semilinear Heat Equation with Nonlinearities Involving Gradient Terms," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 245-264, August.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:2:d:10.1023_a:1017515027783
    DOI: 10.1023/A:1017515027783
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    References listed on IDEAS

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    1. L. A. Fernández & E. Zuazua, 1999. "Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 307-328, May.
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    Cited by:

    1. G. Wang & L. Wang, 2003. "The Carleman Inequality and Its Application to Periodic Optimal Control Governed by Semilinear Parabolic Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 429-461, August.

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