Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero, Jean-Pierre Puel (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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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,...