Existence of beam-equation solutions with strong damping and $p(x)$-biharmonic operator
Mathematica Moravica, Tome 26 (2022) no. 2.

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In this paper, we consider a nonlinear beam equation with a strong damping and the $p(x)$-biharmonic operator. The exponent $p(\cdot)$ of nonlinearity is a given function satisfying some condition to be specified. Using Faedo-Galerkin method, the local and global existence of weak solutions is established with mild assumptions on the variable exponent $p(\cdot)$. This work improves and extends many other results in the literature.
Mots-clés : $p(x)$-biharmonic operator, weak solutions, beam equation, variable exponent. 
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     author = {Jorge Ferreira and Willian S. Panni and Erhan Pi\c{s}kin and Mohammad Shahrouzi},
     title = {Existence of beam-equation solutions with strong damping and $p(x)$-biharmonic operator},
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Jorge Ferreira; Willian S. Panni; Erhan Pişkin; Mohammad Shahrouzi. Existence of beam-equation solutions with strong damping and $p(x)$-biharmonic operator. Mathematica Moravica, Tome 26 (2022) no. 2. https://geodesic-test.mathdoc.fr/item/MM3_2022_26_2_a7/