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    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/120131
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/120131

    Title: On global solutions and blow-up of solutions for a nonlinearly damped Petrovsky system
    Authors: Wu, Shun-Tang
    Tsai, Long-Yi
    Contributors: 應數系
    Date: 2009-04
    Issue Date: 2018-09-25 16:23:07 (UTC+8)
    Abstract: 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].
    Relation: Taiwanese Journal of Mathematics, Vol. 13, No. 2A, pp. 545-558
    AMS MathSciNet:MR2500006
    Data Type: article
    DOI 連結: http://dx.doi.org/10.11650/twjm/1500405355
    DOI: 10.11650/twjm/1500405355
    Appears in Collections:[應用數學系] 期刊論文

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