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Blow-up of solution for a nonlinear Petrovsky type equation with memory

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  • Li, Fushan
  • Gao, Qingyong

Abstract

In this paper, we consider the nonlinear Petrovsky type equation utt+Δ2u−∫0tg(t−s)Δ2u(t,s)ds+|ut|m−2ut=|u|p−2uwith initial conditions and Dirichlet boundary conditions. Under suitable conditions of the initial data and the relaxation function, we prove that the solution with upper bounded initial energy blows up in finite time. Moreover, for the linear damping case, we show that the solution blows up in finite time by different method for nonpositive initial energy.

Suggested Citation

  • Li, Fushan & Gao, Qingyong, 2016. "Blow-up of solution for a nonlinear Petrovsky type equation with memory," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 383-392.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:383-392
    DOI: 10.1016/j.amc.2015.11.018
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    Cited by:

    1. Lishan Liu & Fenglong Sun & Yonghong Wu, 2020. "Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy," Partial Differential Equations and Applications, Springer, vol. 1(5), pages 1-18, October.
    2. Xu, Qingzhen & Huang, Guangyi & Yu, Mengjing & Guo, Yanliang, 2020. "Fall prediction based on key points of human bones," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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