# American Institute of Mathematical Sciences

September & December  2018, 8(3&4): 777-787. doi: 10.3934/mcrf.2018034

## Feedback stabilization with one simultaneous control for systems of parabolic equations

 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)

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

Received  November 2017 Revised  March 2018 Published  September 2018

Fund Project: 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.

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.

Citation: Cătălin-George Lefter, Elena-Alexandra Melnig. Feedback stabilization with one simultaneous control for systems of parabolic equations. Mathematical Control & Related Fields, 2018, 8 (3&4) : 777-787. doi: 10.3934/mcrf.2018034
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