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Exact internal controllability for the semilinear heat equation

Journal Article


Abstract


  • Using the Browder-Minty surjective theorem from the theory of monotone operators, we consider the exact internal controllability for the semilinear heat equation. We show that the system is exactly controllable in L2(Ω) if the nonlinearities are globally Lipschitz continuous. Furthermore, we prove that the controls depend Lipschitz continuously on the terminal states, and discuss the behaviour of the controls as the nonlinear terms tend to zero in some sense. A variant of the Hubert Uniqueness Method is presented to cope with the nonlinear nature of the problem. © 1997 Academic Press.

Publication Date


  • 1997

Citation


  • Liu, W., & Williams, G. H. (1997). Exact internal controllability for the semilinear heat equation. Journal of Mathematical Analysis and Applications, 211(1), 258-272. doi:10.1006/jmaa.1997.5459

Scopus Eid


  • 2-s2.0-0031172972

Web Of Science Accession Number


Start Page


  • 258

End Page


  • 272

Volume


  • 211

Issue


  • 1

Abstract


  • Using the Browder-Minty surjective theorem from the theory of monotone operators, we consider the exact internal controllability for the semilinear heat equation. We show that the system is exactly controllable in L2(Ω) if the nonlinearities are globally Lipschitz continuous. Furthermore, we prove that the controls depend Lipschitz continuously on the terminal states, and discuss the behaviour of the controls as the nonlinear terms tend to zero in some sense. A variant of the Hubert Uniqueness Method is presented to cope with the nonlinear nature of the problem. © 1997 Academic Press.

Publication Date


  • 1997

Citation


  • Liu, W., & Williams, G. H. (1997). Exact internal controllability for the semilinear heat equation. Journal of Mathematical Analysis and Applications, 211(1), 258-272. doi:10.1006/jmaa.1997.5459

Scopus Eid


  • 2-s2.0-0031172972

Web Of Science Accession Number


Start Page


  • 258

End Page


  • 272

Volume


  • 211

Issue


  • 1