Abstract
In this work, we investigate the following nonlinear Timoshenko equation with variable exponents: utt+△2u−M▽uL2(Ω)2△u+utpx−2ut=uqx−2u.By using the Faedo–Galerkin method, we prove the local existence of the solution under suitable conditions. We also investigate the nonexistence of solutions with negative initial energy.
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