Global existence and blow-up of solutionsfor a higher-order kirchhoff-type equation with nonlinear dissipation
Global existence and blow-up of solutionsfor a higher-order kirchhoff-type equation with nonlinear dissipation
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DOI：
10.1016/j.am1.2003.07.014
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发表时间：
2004-12
期刊：
影响因子：
--
通讯作者：
Fucai Li
中科院分区：
文献类型：
--
作者：
Fucai Li
研究了有界域上具有非线性耗散的高阶kirchhoff型方程，其中m < 1为正整数，q, p, r < 0为正常数。我们得到了当p≤r时解整体存在，而如果p > max{r, 2q}，则对于任何初始能量为负的初始数据，解在Lp+2范数有限时间爆破。
This paper deals with the higher-order Kirchhoff-type equation with nonlinear dissipationin a bounded domain, where m < 1 is a positive integer, q, p, r < 0 arepositive constants. We obtain that the solution exists globally if p ≤ r, while ifp > max{r, 2q}, then for any initial data with negative initial energy, the solution blowsup at finite time in Lp+2 norm.