Boundary feedback stabilization of Fisher’s equation

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• 作者：Hanbing Liu^a ; ^{hanbing272003@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Peng Hu^a ; Ionuţ Munteanu^b
• 关键词：Fisher&rsquo ; s equation ; Local stabilization ; Boundary feedback controller
• 刊名：Systems & Control Letters
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：97
• 期：Complete
• 页码：55-60
• 全文大小：836 K

文摘

The aim of this work is to design an explicit finite dimensional boundary feedback controller for locally exponentially stabilizing the equilibrium solutions to Fisher’s equation in both L²(0,1)$L^2(0,1)$ and H¹(0,1)$H^1(0,1)$. The feedback controller is expressed in terms of the eigenfunctions corresponding to unstable eigenvalues of the linearized equation. This stabilizing procedure is applicable for any level of instability, which extends the result of Barbu (2013) for nonlinear parabolic equations. The effectiveness of the approach is illustrated by a numerical simulation.