Stability for extensible beams with a single degenerate nonlocal damping of Balakrishnan-Taylor type

In this paper, motivated by recent papers on the stabilization of evolution problems with nonlocal degenerate damping terms, we address an extensible beam model with degenerate nonlocal damping of Balakrishnan-Taylor type. We discuss initially on the well-posedness with respect to weak and regular s...

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Bibliographic Details
Published in:Journal of Differential Equations 2021-07, Vol.290, p.197-222
Main Authors: Cavalcanti, M.M., Domingos Cavalcanti, V.N., Jorge Silva, M.A., Narciso, V.
Format: Article
Language:English
Subjects:
Balakrishnan-Taylor damping
Beam equation
Degenerate dissipation
Stability
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Summary:In this paper, motivated by recent papers on the stabilization of evolution problems with nonlocal degenerate damping terms, we address an extensible beam model with degenerate nonlocal damping of Balakrishnan-Taylor type. We discuss initially on the well-posedness with respect to weak and regular solutions. Then we show for the first time how hard is to guarantee the stability of the energy solution (related to regular solutions) in the scenarios of constant and non-constant coefficient of extensibility. The degeneracy (in time) of the single nonlocal damping coefficient and the methodology employed in the stability approach are the main novelty for this kind of beam models with degenerate damping.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2021.04.028