Feedback stabilization of the Cahn-Hilliard type system for phase separation

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• 作者：Viorel Barbu^a ; ^vb41@uaic.ro ; Pierluigi Colli^b ; ^{pierluigi.colli@unipv.it} ; Gianni Gilardi^b ; ^{gianni.gilardi@unipv.it} ; Gabriela Marinoschi^c ; ^{gabriela.marinoschi@acad.ro}
• 关键词：93D15 ; 35K52 ; 35Q79 ; 35Q93 ; 93C20
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2286-2334
• 全文大小：566 K
• 卷排序：262

文摘

This article is concerned with the internal feedback stabilization of the phase field system of Cahn–Hilliard type, modeling the phase separation in a binary mixture. Under suitable assumptions on an arbitrarily fixed stationary solution, we construct via spectral separation arguments a feedback controller having its support in an arbitrary open subset of the space domain, such that the closed loop nonlinear system exponentially reaches the prescribed stationary solution. This feedback controller has a finite dimensional structure in the state space of solutions. In particular, every constant stationary solution is admissible.