@article{Hajjej2023, 
author = {Zayd Hajjej},
title = {Asymptotic stability for solutions of a coupled system of quasi-linear viscoelastic Kirchhoff plate equations},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {6},
pages = {3471-3494},
keywords = {Kirchhoff plate equation, free boundary conditions, viscoelastic, Faedo-Galerkin method, asymptotic stability},
url = {https://www.sciopen.com/article/10.3934/era.2023176},
doi = {10.3934/era.2023176},
abstract = {In this manuscript, we study the asymptotic stability of solutions of two coupled quasi-linear viscoelastic Kirchhoff plate equations involving free boundary conditions, and accounting for rotational forces                                           |                  y          t                          |                      ρ                                    y                      t            t                          −        Δ                  y                      t            t                          +                  Δ                      2                          y        −                  ∫          0          t                          h          1                (        t        −        s        )                  Δ          2                y        (        s        )                d        s        +                  f          1                (        y        ,        z        )        =        0        ,                                                              |                  z          t                          |                      ρ                                    z                      t            t                          −        Δ                  z                      t            t                          +                  Δ                      2                          z        −                  ∫          0          t                          h          2                (        t        −        s        )                  Δ          2                z        (        s        )                d        s        +                  f          2                (        y        ,        z        )        =        0.            The system under study in this contribution could be seen as a model for two stacked plates. This work is motivated by previous works about coupled quasi-linear wave equations or concerning single quasi-linear Kirchhoff plate. The existence of local weak solutions is established by the Faedo-Galerkin approach. By using the perturbed energy method, we prove a general decay rate of the energy for a wide class of relaxation functions.}
}