Indirect stabilization on Kirchhoff plates by memory effects

This work is devoted to the study of the asymptotic behavior of a coupled system that describes the vertical displacement of thin Kirchhoff plates. One of the equations has a viscoelastic dissipation of memory type and the other is conservative. The memory depends on a fractional operator with expon...

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Bibliographic Details
Published in:Journal of evolution equations 2023-03, Vol.23 (1), Article 6
Main Authors: Tyszka, Guilherme F., Astudillo, María R., Oquendo, Higidio Portillo
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Coefficients
Decay rate
Inertia
Mathematics
Mathematics and Statistics
Operators (mathematics)
Plates
Polynomials
Rigidity
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Summary:This work is devoted to the study of the asymptotic behavior of a coupled system that describes the vertical displacement of thin Kirchhoff plates. One of the equations has a viscoelastic dissipation of memory type and the other is conservative. The memory depends on a fractional operator with exponent θ ∈ [ 0 , 1 ] and its kernel is an exponentially decreasing function. We obtain explicit optimal polynomial decay rates for the solutions with regular initial data. The decay rates depend on the exponent of the memory and some relations between the mass density, the flexural rigidity coefficients and the coefficients of the rotational inertia terms. Considering equal mass densities, the worst decay rate happens when the rotational inertia coefficients are distinct, while the best decay is only possible when the rotational inertia coefficients coincide as well as the flexural rigidity coefficients.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-022-00855-x