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  4. Mathematical modeling of wave propagation in viscoelastic media with the fractional Zener model

Mathematical modeling of wave propagation in viscoelastic media with the fractional Zener model

MMC.
2021;
Volume 8, Number 4
: pp. 601–615
https://doi.org/10.23939/mmc2021.04.601
Received: May 23, 2021
Accepted: June 07, 2021

Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 601–615 (2021)

Authors:
  1. M. Ait Ichou
  2. H. El Amri
  3. A. Ezziani
1
Laboratory LMA ENS, Hassan II University of Casablanca; Laboratory MAEGE FSJES Aїn Sebaa, Hassan II University of Casablanca
2
Laboratory LMA ENS, Hassan II University of Casablanca
3
Laboratory MAEGE FSJES Aїn Sebaa, Hassan II University of Casablanca

The question of interest for the presented study is the mathematical modeling of wave propagation in dissipative media.  The generalized fractional Zener model in the case of dimension d (d=1,2,3) is considered.  This work is devoted to the mathematical analysis of such model: existence and uniqueness of the strong and weak solution and energy decay result which guarantees the wave dissipation.  The existence of the weak solution is shown using a priori estimates for solutions which are also presented.

fractional derivative
strong solution
weak solution
energy decay
plane waves
viscoelastic waves
Zener's model
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