Feedback stabilization with one simultaneous control for systems of parabolic equations

Cătălin-George Lefter; Elena-Alexandra Melnig

doi:10.3934/mcrf.2018034

Article Contents

2018, Volume 8, Issue 3&4: 777-787. Doi: 10.3934/mcrf.2018034

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Feedback stabilization with one simultaneous control for systems of parabolic equations

Cătălin-George Lefter^, and
Elena-Alexandra Melnig

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

* Corresponding author: Cătălin-George Lefter (catalin.lefter@uaic.ro)
* Corresponding author: Cătălin-George Lefter (catalin.lefter@uaic.ro)

Dedicated to Professor Jiongmin Yong on the occasion of his 60th anniversary

Received: November 2017

Revised: March 2018

Published: September 2018

The second 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

In this work controlled systems of semilinear parabolic equations are considered. Only one control is acting in both equations and it is distributed in a subdomain. Local feedback stabilization is studied. The approach is based on approximate controllability for the linearized system and the use of an appropriate norm obtained from a Lyapunov equation. Applications to reaction-diffusion systems are discussed.

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

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