[1]李刚,于勇.一类非线性波动方程整体解的不存在性[J].东南大学学报(自然科学版),2004,34(5):690-693.[doi:10.3969/j.issn.1001-0505.2004.05.029]
 Li Gang,Yu Yong.Global nonexistence for a nonlinear wave equation[J].Journal of Southeast University (Natural Science Edition),2004,34(5):690-693.[doi:10.3969/j.issn.1001-0505.2004.05.029]
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一类非线性波动方程整体解的不存在性()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
34
期数:
2004年第5期
页码:
690-693
栏目:
数学、物理学、力学
出版日期:
2004-09-20

文章信息/Info

Title:
Global nonexistence for a nonlinear wave equation
作者:
李刚1于勇2
1 东南大学数学系, 南京 210096; 2 南京气象学院数学系, 南京 210044
Author(s):
Li Gang1 Yu Yong2
1 Department of Mathematics, Southeast University, Nanjing 210096, China
2 Department of Mathematics, Nanjing Institute of Meteorology, Nanjing 210044, China
关键词:
波动方程 Potential Well Sobolev-Hardy不等式 整体解的不存在性
Keywords:
wave equation Potential Well Sobolev-Hardy inequality global nonexistence
分类号:
O175.29
DOI:
10.3969/j.issn.1001-0505.2004.05.029
摘要:
运用Potential Well方法研究了一类四阶非线性波动方程初边值问题整体解的不存在性.首先定义了该问题的位势深度d,然后运用索伯列夫空间中的嵌入定理结合Sobolev-Hardy不等式证明位势深度d>0,再恰当地构造能量函数E(t),运用反证法证明了该问题整体解的不存在性.当初值满足K(u0)<00,J(u0)<d,E(00)<d时,该问题没有整体解.这里的K(·)J(·)是2个泛函.
Abstract:
The global nonexistence of a fourth order wave equation is studied using Potential Well method. Potential depth of this problem is defined first. By using Sobolev-Hardy inequality and the theory of embedding in Sobolev space, it is proved that the potential depth is a positive number. Finally, the energy function E(t) is appropriately constructed global nonexistence is verified by using reduction to absurdity. It is shown that the problem has no global solution when its initial value satisfy K(u0)<00,J(u0)<d,E(00)<d. Here K(·) and J(·)are two functions.

参考文献/References:

[1] Varlamov V.On the damped Boussinesq equation in a circle [J].Non Ana, 1999,38:447-470.
[2] Ghoussoub N,Yuan C.Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents [J]. Trans Amer Math Soc, 2000,352(12):5703-5743.
[3] 陈才生.一类非线性梁方程整体解的不存在性[J].南京大学学报数学半年刊.2002,19(2):247-254.
  Chen Caisheng.Global nonexistence of nonlinear beam equation[J].Journal of Nanjing University Mathematical Biquarterly, 2002,19(2):247-254.(in Chinese)
[4] Todorova G.Stable and unstable sets for the Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms [J].J Math Ana and App, 1999,239:213-226.

备注/Memo

备注/Memo:
作者简介: 李刚(1958—),男,硕士,副教授,硕士生导师,ligang@njim.edu.cn.
更新日期/Last Update: 2004-09-20