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    题名: On global solutions and blow-up of solutions for a nonlinearly damped Petrovsky system
    作者: Wu, Shun-Tang
    蔡隆義
    Tsai, Long-Yi
    贡献者: 應數系
    日期: 2009-04
    上传时间: 2018-09-25 16:23:07 (UTC+8)
    摘要: We consider an initial-boundary value problem for a Petrovskiĭ equation, with nonlinear damping, of the form $$u_{tt}+\\Delta^2u+a|u_t|^{m-2}u_t=b|u|^{p-2}u$$

    in a bounded domain. We show that solutions are global in time under some conditions without any relations between $m$ and $p$. We also prove that local solutions blow up in finite time if $p>m$ and the initial energies are nonnegative. Decay estimates for the energy functionals and estimates for the life-span of solutions are given. In this way, we can extend the result in [S. A. Messaoudi, J. Math. Anal. Appl. 265 (2002), no. 2, 296–308; MR1876141].
    關聯: Taiwanese Journal of Mathematics, Vol. 13, No. 2A, pp. 545-558
    AMS MathSciNet:MR2500006
    数据类型: article
    DOI 連結: http://dx.doi.org/10.11650/twjm/1500405355
    DOI: 10.11650/twjm/1500405355
    显示于类别:[應用數學系] 期刊論文

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