华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (3): 149-163，175.

• 应用数学与基础数学 • 上一篇    下一篇

非线性~$p(x)$-Kirchhoff~方程在动态边界条件下的非全局存在性~

李细柳1,  穆春来1,  曾 嵘2, 周寿明1   

  1. 1. 重庆大学 数学与统计学院, 重庆 401331；2. 西南财经大学 经济数学学院, 成都 611130
  • 收稿日期:2012-04-01 修回日期:2012-07-01 出版日期:2013-05-25 发布日期:2013-07-10

Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions

LI Xi-liu1, MU Chun-lai1, ZENG Rong2, ZHOU Shou-ming1   

  1. 1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;  2. School of Economic Mathematics, Southwestern
    University of Finance and Economics, Chengdu 611130, China
  • Received:2012-04-01 Revised:2012-07-01 Online:2013-05-25 Published:2013-07-10

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摘要： 考虑在动态边界条件下,
非线性~$p$($x$)-Kirchhoff~方程组解的非全局存在性,
该方程组带有非线性外力项~$Q$~和非线性源项$~f$.
通过研究方程组解的自然能量, 证明在初始能量小于一个临界值时,
方程组解的非全局存在性.
并将带有拟线性齐次~$p$-拉普拉斯算子的~$p$-Kirchhoff~方程组推广到~$p(x)$-Kirchhoff~方程组,
该方程组近年被用来模拟很多现象.

关键词: p(x)$-Kirchhoff~方程组, 非全局存在性, 非线性源项和外力项

Abstract: This paper considered the global non-existence of solutions
of nonlinear $p(x)$-Kirchhoff systems with dynamic boundary
conditions, which involve nonlinear external damping terms $Q$ and
nonlinear driving forces $f$. Through the study of the natural
energy associated to the solutions $u$ of the systems, the
nonexistence of global solutions, when the initial energy is
controlled above by a critical value was proved. And the
$p$-Kirchhoff equations involving the quasilinear homogeneous
$p$-Laplace operator were extended to the $p(x)$-Kirchhoff equations
which have been used in the last decades to model various
phenomena.

Key words: $p(x)$-Kirchhoff systems, global non-existence, nonlinear source and boundary damping terms

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