Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
Dpto. E.D.A.N., University of Sevilla,
Aptdo. 1160, 41080 Sevilla, Spain; email@example.com;
2 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75035 Cedex 05, Paris, France; firstname.lastname@example.org
3 Laboratoire de Mathématiques Appliquées, Université de Versailles – St. Quentin, 45 avenue des États-Unis, 78035 Versailles, France; email@example.com
Revised: 30 May 2005
Revised: 13 June 2005
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 . 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.
Mathematics Subject Classification: 35K20 / 93B05
Key words: Controllability / heat equation / Fourier boundary conditions / semilinear.
© EDP Sciences, SMAI, 2006