Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case
ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 3, pp. 466-483.

This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form y n+f(y)=0. We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one has exact controllability to the trajectories.

DOI: 10.1051/cocv:2006011
Classification: 35K20,  93B05
Keywords: controllability, heat equation, Fourier boundary conditions, semilinear
Fernández-Cara, Enrique ; González-Burgos, Manuel ; Guerrero, Sergio 1; Puel, Jean-Pierre 2

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France;
2 Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; ; Laboratoire de Mathématiques Appliquées, Université de Versailles, St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France;
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     author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and Guerrero, Sergio and Puel, Jean-Pierre},
     title = {Exact controllability to the trajectories of the heat equation with {Fourier} boundary conditions : the semilinear case},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {466--483},
     publisher = {EDP-Sciences},
     volume = {12},
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Fernández-Cara, Enrique; González-Burgos, Manuel; Guerrero, Sergio; Puel, Jean-Pierre. Exact controllability to the trajectories of the heat equation with Fourier boundary conditions : the semilinear case. ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 3, pp. 466-483. doi : 10.1051/cocv:2006011. http://www.numdam.org/articles/10.1051/cocv:2006011/

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