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[1] Chen Caisheng, Ren Lei,. Weak solution for a fourth-order nonlinear wave equation [J]. Journal of Southeast University (English Edition), 2005, 21 (3): 369-374. [doi:10.3969/j.issn.1003-7985.2005.03.024]
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Weak solution for a fourth-order nonlinear wave equation()
一类四阶波动方程的弱解
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
21
Issue:
2005 3
Page:
369-374
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2005-09-30

Info

Title:
Weak solution for a fourth-order nonlinear wave equation
一类四阶波动方程的弱解
Author(s):
Chen Caisheng Ren Lei
College of Science, Hohai University, Nanjing 210098, China
陈才生 任磊
河海大学理学院, 南京 210098
Keywords:
nonlinear wave equation uniqueness energy decay estimate blow up
非线形波动方程 惟一性 能量衰减估计 爆破
PACS:
O175.29
DOI:
10.3969/j.issn.1003-7985.2005.03.024
Abstract:
The existence and the nonexistence, the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation uttΔ2 u-butΔu+ut|ut|r+g(u)=0 in Ω×(0, )are studied with the boundary condition u=(əu)/(əυ)=0 on əΩ and the initial condition u(x, 0)=u00(x), ut(x, 0)=u11(x, 0)in bounded domain Ω⊂Rn , n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory, and the existence of the solution is gotten by the Galekin approximation method.
研究下列初边值问题:uttΔ2u-but+ut|ut|r+g(u)=0 in Ω×(0, );u(x, 0)=u00(x), ut(x, 0)=u11(x, 0), x∈Ω; u=(əu)/(əυ), x∈əΩ的整体解的存在性和不存在性, 以及整体解的惟一性和能量估计.这里ΩRn(n≥1)中的有界区域.借助于乘子方程, 推出了整体解的能量衰减率.借助于势井理论, 得到了在有限时刻内爆破的充分条件.由Galekin 近似方法得到解的存在性.

References:

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Memo

Memo:
Biography: Chen Caisheng(1956—), male, professor, cshengchen@hhu.edu.cn.
Last Update: 2005-09-20