Control of three heat equations coupled with two cubic nonlinearities

Jean-Michel Coron (1) , Jean-Philippe Guilleron (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We study the null controllability of three parabolic equations. The control is acting only on one of the three equations. The three equations are coupled by means of two cubic nonlinearities. The linearized control system around 0 is not null controllable. However, using the cubic nonlinearities, we prove the (global) null controllability of the control system. The proof relies on the return method, an algebraic solvability and smoothing properties of the parabolic equations.

Mots clés: null controllability; parabolic systems; return method

Domaines: Optimisation et contrôle [math.OC]

Jean-Michel Coron, Jean-Philippe Guilleron. Control of three heat equations coupled with two cubic nonlinearities. SIAM Journal on Control and Optimization, 2017, 55 (2), pp.989-1019. ⟨10.1137/15M1041201⟩. ⟨hal-01401056⟩