Internal feedback stabilization for parabolic systems coupled in zero or first order terms

Elena-Alexandra Melnig

doi:10.3934/eect.2020069

Article Contents

2021, Volume 10, Issue 2: 333-351. Doi: 10.3934/eect.2020069

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Internal feedback stabilization for parabolic systems coupled in zero or first order terms

Elena-Alexandra Melnig^1,2,

1.
Faculty of Mathematics, University "Al. I. Cuza" Iaşi, Romania
2.
Octav Mayer Institute of Mathematics, Romanian Academy, Iaşi Branch, Romania

Received: December 31, 2019

Revised: February 29, 2020

Early access: June 2020

Published: June 2021

The author was supported by a grant of the Ministry of Research and Innovation, CNCS - UEFISCDI, project number PN-III-P4-ID-PCE-2016-0011

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Abstract

We consider systems of $ n $ parabolic equations coupled in zero or first order terms with $ m $ scalar controls acting through a control matrix $ B $. We are interested in stabilization with a control in feedback form. Our approach relies on the approximate controllability of the linearized system, which in turn is related to unique continuation property for the adjoint system. For the unique continuation we establish algebraic Kalman type conditions.

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Mathematics Subject Classification: Primary: 35K40, 93D15, 93B52; Secondary: 35K57, 93B18.

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