Geodesic
Existence and stability results of a nonlinear Timoshenko equation with damping and source terms
Theoretical and applied mechanics, Tome 48 (2021) no. 1.

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In this paper, we consider a nonlinear Timoshenko equation. First, we prove the local existence solution by the Faedo--Galerkin method, and, under suitable assumptions with positive initial energy, we prove that the local existence is global in time. Finally, the stability result is established based on Komornik's integral inequality.
Keywords: Timoshenko equation, Faedo-Galerkin method, global existence, stability solution 
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     author = {Amar Ouaoua and Aya Khaldi and Messaoud Maouni},
     title = {Existence and stability results of a nonlinear {Timoshenko} equation with damping and source terms},
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     pages = {53 - 66},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/TAM_2021_48_1_a3/}
}
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Amar Ouaoua; Aya Khaldi; Messaoud Maouni. Existence and stability results of a nonlinear Timoshenko equation with damping and source terms. Theoretical and applied mechanics, Tome 48 (2021) no. 1. http://geodesic.mathdoc.fr/item/TAM_2021_48_1_a3/