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Levine, H.A. (1974) Instability and Nonexistence of Global Solutions of Nonlinear Wave Equation of the Form Putt = Au + F(u). Transactions of the American Mathematical Society, 192, 1-21.

has been cited by the following article:

• TITLE: Blow Up and Global Existence for a Nonlinear Viscoelastic Wave Equation with Strong Damping and Nonlinear Damping and Source terms

  AUTHORS: Liang Guo, Zhaoqin Yuan, Guoguang Lin

  KEYWORDS: Viscoelastic Equation, Blow Up, Global Existence

  JOURNAL NAME: Applied Mathematics, Vol.6 No.5, May 14, 2015

  ABSTRACT: In this paper, we consider an initial-boundary value problem for a nonlinear viscoelastic wave equation with strong damping, nonlinear damping and source terms. We proved a blow up result for the solution with negative initial energy if p > m, and a global result for p ≤ m.