In this paper we will analyze the controllability properties of a linear coupled parabolic system of m equations when a unique distributed control is exerted on the system. We will see that, when a cascade system is considered, we can prove a global Carleman inequality for the adjoint system which bounds the global integrals of the variable φ = (φ1, …, φm)* in terms of a unique localized variable. As a consequence, we will obtain the null controllability property for the system with one control force.
Cite this article
Manuel González-Burgos, Luz de Teresa, Controllability results for cascade systems of <var>m</var> coupled parabolic PDEs by one control force. Port. Math. 67 (2010), no. 1, pp. 91–113DOI 10.4171/PM/1859