Blow-up for the Timoshenko-type equation with variable exponents. (June 2023)

• Record Type: Journal Article
• Authors: Ding, Hang; Zhou, Jun
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: Timoshenko equation -- Variable exponents -- Blow-up -- Blow-up time -- Arbitrarily high initial energy; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103801
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The finite time blow-up of solutions to a nonlinear Timoshenko-type equation with variable exponents is studied. More concretely, we prove that the solutions blow up in finite time with positive initial energy. Also, the existence of finite time blow-up solutions with arbitrarily high initial energy is established. Meanwhile, the upper and lower bounds of the blow-up time are derived. These results deepen and generalize the ones obtained in [Nonlinear Anal. Real World Appl., 61: Paper No. 103341, 2021].