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Local Null Controllability of a Free-Boundary Problem for the Semilinear 1D Heat Equation

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Abstract

This paper deals with the local null control of a free-boundary problem for the 1D semilinear heat equation with distributed controls (locally supported in space) or boundary controls (acting at \(x=0\)). In the main result we prove that, if the final time T is fixed and the initial state is sufficiently small, there exists controls that drive the state exactly to rest at time \(t=T\).

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Authors and Affiliations

  1. Dpto. E.D.A.N., Univ. Sevilla, Aptdo. 1160, 41080, Seville, Spain

    Enrique Fernández-Cara

  2. Dpto. Matemática, Univ. Federal do Ceará, Fortaleza, CE, Brazil

    Ivaldo Tributino de Sousa

Authors
  1. Enrique Fernández-Cara
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  2. Ivaldo Tributino de Sousa
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Correspondence to Ivaldo Tributino de Sousa.

Additional information

Enrique Fernández-Cara is partially supported by Grant MTM2013-41286-P (DGI-MINECO, Spain) and CAPES (Brazil).

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Fernández-Cara, E., de Sousa, I.T. Local Null Controllability of a Free-Boundary Problem for the Semilinear 1D Heat Equation. Bull Braz Math Soc, New Series 48, 303–315 (2017). https://doi.org/10.1007/s00574-016-0001-0

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  • DOI: https://doi.org/10.1007/s00574-016-0001-0

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