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題名 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
貢獻者 應數系
日期 2009-04
上傳時間 25-Sep-2018 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
資料類型 article
DOI http://dx.doi.org/10.11650/twjm/1500405355
dc.contributor 應數系
dc.creator (作者) Wu, Shun-Tang
dc.creator (作者) 蔡隆義
dc.creator (作者) Tsai, Long-Yi
dc.date (日期) 2009-04
dc.date.accessioned 25-Sep-2018 16:23:07 (UTC+8)-
dc.date.available 25-Sep-2018 16:23:07 (UTC+8)-
dc.date.issued (上傳時間) 25-Sep-2018 16:23:07 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/120131-
dc.description.abstract (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].
en_US
dc.format.extent 112 bytes-
dc.format.mimetype text/html-
dc.relation (關聯) Taiwanese Journal of Mathematics, Vol. 13, No. 2A, pp. 545-558
dc.relation (關聯) AMS MathSciNet:MR2500006
dc.title (題名) On global solutions and blow-up of solutions for a nonlinearly damped Petrovsky system
dc.type (資料類型) article
dc.identifier.doi (DOI) 10.11650/twjm/1500405355
dc.doi.uri (DOI) http://dx.doi.org/10.11650/twjm/1500405355