@article{Al-Gharabli2022, 
author = {Mohammad M. Al-Gharabli and Adel M. Al-Mahdi},
title = {Existence and stability results of a plate equation with nonlinear damping and source term},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {11},
pages = {4038-4065},
keywords = {plate equation, Galerkin method, Banach fixed point theorem, general decay, nonlinear frictional damping},
url = {https://www.sciopen.com/article/10.3934/era.2022205},
doi = {10.3934/era.2022205},
abstract = {The main goal of this work is to investigate the following nonlinear plate equation         u          t      t        +      Δ    2    u  +  α  (  t  )  g  (      u    t    )  =  u  |  u      |          β        ,which models suspension bridges. Firstly, we prove the local existence using Faedo-Galerkin method and Banach fixed point theorem. Secondly, we prove the global existence by using the well-depth method. Finally, we establish explicit and general decay results for the energy of solutions of the problem. Our decay results depend on the functions    α and    g and obtained without any restriction growth assumption on    g at the origin. The multiplier method, properties of the convex functions, Jensen's inequality and the generalized Young inequality are used to establish the stability results.}
}