Null controllability of a parabolic system with a cubic coupling term

Jean-Michel Coron (1) , Sergio Guerrero (1) , Lionel Rosier (2, 3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 IECN - Institut Élie Cartan de Nancy
3 CORIDA - Robust control of infinite dimensional systems and applications

We consider a system of two parabolic equations with a forcing term present in one equation and a cubic coupling term in the other one. We prove that the system is locally null controllable.

Mots clés: Null controllability; parabolic system; nonlinear coupling; Carleman estimate; return method

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Jean-Michel Coron, Sergio Guerrero, Lionel Rosier. Null controllability of a parabolic system with a cubic coupling term. SIAM Journal on Control and Optimization, 2010, 48 (8), pp.5629-5653. ⟨10.1137/100784539⟩. ⟨hal-00451864⟩