Existence and non-existence of solutions for Timoshenko-type equations with variable exponents. (October 2021) - Antontsev, Stanislav N.; Ferreira, Jorge; Pişkin, Erhan; Cordeiro, Sebastião Martins Siqueira
Abstract: In this work, we investigate the following nonlinear Timoshenko equation with variable exponents: u t t + △ 2 u − M ▽ u L 2 ( Ω ) 2 △ u + u t p x − 2 u t = u q x − 2 u . 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.