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Uniform stabilization of a one‐dimensional hybrid thermo‐elastic structure
Author(s) -
Dalsen Marié GrobbelaarVan
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.415
Subject(s) - mathematics , inertia , operator (biology) , lyapunov function , mathematical analysis , stability (learning theory) , classical mechanics , physics , computer science , biochemistry , chemistry , repressor , transcription factor , gene , nonlinear system , quantum mechanics , machine learning
This paper is concerned with the stabilization of a one‐dimensional hybrid thermo‐elastic structure consisting of an extensible thermo‐elastic beam which is hinged at one end with a rigid body attached to its free end. The model takes account of the effect of stretching on bending and rotational inertia. The property of uniform stability of the energy associated with the model is asserted by constructing an appropriate Lyapunov functional for an abstract second order evolution problem. Critical use is made of a multiplier of an operator theoretic nature, which involves the fractional power A −1/2 of the bi‐harmonic operator pair A acting in the abstract evolution problem. An explicit decay rate of the energy is obtained. Copyright © 2003 John Wiley & Sons, Ltd.