Blow-up phenomena for a damped plate equation with logarithmic nonlinearity. (June 2023)

• Record Type: Journal Article
• Authors: Li, Xiatong; Fang, Zhong Bo
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: Damped plate equation -- Logarithmic nonlinearity -- Blow-up -- Lifespan; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103823
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the finite time blow-up phenomena for a damped plate equation with logarithmic nonlinearity under the Navier boundary condition. Combining potential well method and modified differential inequality technique, we establish the finite time blow-up properties of solutions with low initial energy E ( 0 ) ≤ d and high energy. In particular, we consider the case where the initial displacement and initial velocity have the same ( ∫ Ω u 0 u 1 d x > 0 ) or different signs ( ∫ Ω u 0 u 1 d x > − ‖ u 0 ‖ ∗ 2 2 ) in the sense of L 2 inner product at high energy level. Moreover, the lower bounds for the blow-up time in subcritical, critical, supercritical and ultra-supercritical cases are also derived.