Existence and non-existence of solutions for Timoshenko-type equations with variable exponents. (October 2021)

• Record Type: Journal Article
• Authors: Antontsev, Stanislav N.; Ferreira, Jorge; Pişkin, Erhan; Cordeiro, Sebastião Martins Siqueira
• Is Part Of: Nonlinear analysis. Volume 61(2021)
• Publication Date: 2021-10
• Subjects: Local existence -- Nonexistence -- Timoshenko equation -- Variable exponent; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103341
• Languages: English
• ISSNs: 1468-1218

Abstract

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.