Energy decay of a microbeam model with a locally distributed nonlinear feedback control

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:467

Article

Guzman, Patricio^1,2 

[1] Univ Chile, Fac Ciencias Fis & Matemat, Dept Ingn Matemat, Santiago, Chile

[2] Univ Chile, Fac Ciencias Fis & Matemat, Ctr Modelamiento Matemat, Santiago, Chile

关键词: Microbeam model;    Hyperbolic equation;    Internal stabilization;    Nonlinear feedback control;    Exponential energy decay;    Polynomial energy decay;   

DOI  :  10.1016/j.jmaa.2018.07.006

来源: Elsevier

【 摘 要 】

In this paper we address the problem of internal stabilization of the deflection of a microbeam, which is modeled by a sixth-order hyperbolic equation. Employing multiplier techniques and an integral inequality, we prove that a locally distributed nonlinear feedback control forces the energy associated to the deflection to decay exponentially or polynomially to zero. As a consequence of this, the deflection goes to the rest position as the time goes to infinity. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free