Null controllability of the semilinear heat equation
E. Fernández-Cara (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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E. Fernández-Cara (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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Lionel Rosier (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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Alexander Khapalov (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Alexander Y. Khapalov (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain via the coefficient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at infinity the global approximate controllability...
S. Guerrero, O. Yu. Imanuvilov (2007)
Annales de l'I.H.P. Analyse non linéaire
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Jean-Michel Coron (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.
Karine Beauchard (2005-2006)
Séminaire Équations aux dérivées partielles
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One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite...