Blow up of arbitrarily positive initial energy solutions for a viscoelastic wave equation. (December 2015)

• Record Type: Journal Article
• Authors: Song, Haitao
• Is Part Of: Nonlinear analysis. Volume 26(2015)
• Page Start: 306
• Page End: 314
• Publication Date: 2015-12
• Subjects: Blow-up -- Finite time -- Hyperbolic -- Nonlinear damping -- Viscoelastic; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.05.015
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we consider the nonlinear viscoelastic equation: u t t − △ u + ∫ 0 t g ( t − τ ) △ u ( τ ) d τ + | u t | m − 2 u t = | u | p − 2 u, in Ω × [ 0, T ], with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g, we show the finite time blow up of some solutions whose initial data have arbitrarily high initial energy.