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Homogeneity applied to the controllability of a system of parabolic equations

Authors: Jean-Michel Coron, Sergio Guerrero, Philippe Martin and Lionel Rosier, 2015 European Control Conference (ECC 2015), pp. 2470-2475, 15-17 July 2015, Linz.
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.
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BibTeX:
@Proceedings{2016-01-28,
author = {Jean-Michel Coron, Sergio Guerrero, Philippe Martin and Lionel Rosier},
editor = {},
title = {Homogeneity applied to the controllability of a system of parabolic equations},
booktitle = {2015 European Control Conference (ECC 2015)},
volume = {},
publisher = {},
address = {Linz},
pages = {2470-2475},
year = {2015},
abstract = {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.},
keywords = {}}