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Chevron Pattern Equations: Exponential Attractor and Global Stabilization

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 29 Apr 2021Embargo end date: 01 Jan 2021 Turkey Publisher:Springer Science and Business Media LLCJournal:Vietnam Journal of Mathematics, volume 49, pages 901-918 (issn: 2305-221X, eissn: 2305-2228, Copyright policy )
Authors: Habiba Kalantarova; Varga Kalantarov; Orestis Vantzos;

doi: 10.1007/s10013-021-00486-8 , 10.48550/arxiv.2102.04529

arXiv: http://arxiv.org/abs/2102.04529

Chevron Pattern Equations: Exponential Attractor and Global Stabilization

Abstract

The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state solution through application of a finite-dimensional feedback control is proved in two spatial dimensions. The stabilization of an arbitrary fixed solution is shown in one spatial dimension along with relevant numerical results.

Country
Turkey
Related Organizations
Keywords

Finite differences, Feedback stabilization, Chevron patterns, Exponential attractor, Fourier modes, Chevron patterns; Feedback stabilization; Exponential attractor; Fourier modes; Finite differences, 35K55, 35B41, 49N60, 76A15, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics, Analysis of PDEs (math.AP)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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bronze