Open AccessEnergy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping
Author(s) -
Mohammad Akil,
Ibtissam Issa,
Ali Wehbe
Publication year - 2023
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021059
Subject(s) - mathematical analysis , mathematics , fractional calculus , multiplier (economics) , beam (structure) , boundary value problem , physics , wave equation , boundary (topology) , bernoulli's principle , euler's formula , optics , economics , macroeconomics , thermodynamics
In this paper, we investigate the energy decay of hyperbolic systems of wave-wave, wave-Euler-Bernoulli beam and beam-beam types. The two equations are coupled through boundary connection with only one localized non-smooth fractional Kelvin-Voigt damping. First, we reformulate each system into an augmented model and using a general criteria of Arendt-Batty, we prove that our models are strongly stable. Next, by using frequency domain approach, combined with multiplier technique and some interpolation inequalities, we establish different types of polynomial energy decay rate which depends on the order of the fractional derivative and the type of the damped equation in the system.