一类四阶非线性波动方程的初值问题

陈国旺; 侯长顺

一类四阶非线性波动方程的初值问题

陈国旺¹,
侯长顺²

1.
郑州大学数学系,郑州 450052;2.河南工业大学理学院,郑州 450052

基金项目: 国家自然科学基金资助项目(10671182)

详细信息

作者简介:
陈国旺(1935- ),男,河北万全人,教授,博士(联系人.E-mail:chenguowang@zzu.edu.cn).

中图分类号: O175.29；O175.27
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- 被引次数: 0
出版历程
- 收稿日期: 2008-08-11
- 修回日期: 2009-01-16
- 刊出日期: 2009-03-15

Initial Value Problem for a Class of Nonlinear Wave Equations of Fourth Order

CHEN Guo-wang¹,
HOU Chang-shun²

1.
Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P. R. China;

摘要

摘要: 应用压缩映射原理和延拓定理，在分数次Sobolev空间中，证明一类四阶非线性波动方程的初值问题，存在唯一的整体广义解和整体古典解．还给出该初值问题解爆破的充分条件．
- 四阶非线性波动方程 /
- 初值问题 /
- 整体解 /
- 解的爆破
Abstract: The existence and the uniqueness of the global generalized solution and the global classical solution to the initial value problem for a class of nonlinear wave equation of fourth order are studied in the fractional order Sobolev space by the contraction mapping principle and the extension theorem. The sufficient conditions for blow up of the solution to the above initial value problem are given.
- nonlinear wave equation of fourth order /
- initial value problem /
- global solution /
- blow up of solution

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参考文献(16)

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