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Exponential stabilization of a microbeam system with a boundary or distributed time delay
Author(s) -
Feng Baowei,
Chentouf Boumediène
Publication year - 2021
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.7518
Subject(s) - microbeam , microscale chemistry , mathematics , boundary (topology) , term (time) , exponential stability , boundary value problem , exponential decay , stability (learning theory) , mathematical analysis , beam (structure) , control theory (sociology) , computer science , control (management) , physics , optics , quantum mechanics , nonlinear system , artificial intelligence , nuclear physics , mathematics education , machine learning
This paper addresses the stabilization problem of a microscale beam system subject to a delay. Several situations are considered depending whether the delay occurs as a boundary or interior/distributed term. In both cases, the microbeam system is shown to be well posed in the sense of semigroups theory of linear operators. More importantly, using the energy method, the exponential stability is established as long as the parameter of the delay term is small.