Homogeneity applied to the controllability of a system of parabolic equations

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

1 LJLL - Laboratoire Jacques-Louis Lions
2 CAS - Centre Automatique et Systèmes

We consider a system of two parabolic equations with a forcing term present in one equation and a nonlinear coupling term of a particular type in the other one. We establish a local null controllability result, even if the linearized control system fails to be null controllable. The proof combines the return method, a Carleman inequality and an argument based on homogeneity. Our result can be applied to a reaction- diffusion system from Chemistry and to the Ginzburg-Landau equation.

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Jean-Michel Coron, Sergio Guerrero, Philippe Martin, Lionel Rosier. Homogeneity applied to the controllability of a system of parabolic equations. 2015 European Control Conference (ECC 2015), Jul 2015, Linz, Austria. pp.2470-2475, ⟨10.1109/ECC.2015.7330909⟩. ⟨hal-01263657⟩