JournalspmVol. 67 / No. 1DOI 10.4171/pm/1859

Controllability results for cascade systems of <var>m</var> coupled parabolic PDEs by one control force

  • Manuel González-Burgos

    Universidad de Sevilla, Spain
  • Luz de Teresa

    Universidad Nacional Autonoma de México, México, D.F., Mexico
Controllability results for cascade systems of <var>m</var> coupled parabolic PDEs by one control force cover

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Abstract

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.