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    Existence and asymptotic behavior of beam-equation solutions with strong damping and p(x)-biharmonic operator
    (B.Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine, 2022) Ferreira, Jorge; Panni, Willian S.; Messaoudi, Salim A.; Pişkin, Erhan; Shahrouzi, Mohammad
    In this paper, we consider a nonlinear beam equation with a strong damping and the p(x)-biharmonic operator. The exponent p(·) of nonlinearity is a given function satisfying some condition to be specified. Applying Faedo– Galerkin’s method, the existence of weak solutions is proved. Using Nakao’s lemma, the asymptotic behavior of weak solutions is established with mild assumptions on the variable exponent p(·). We show the asymptotic behavior of the weak solution is exponentially and algebraically depending on the variable exponent. This work improves and extends many other results in the literature.