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)

[1]	朱位秋.弹性杆中的非线性波[J].固体力学学报, 1980,1(2):247-253.
[2]	庄蔚，杨桂通.孤波在非线性弹性杆中的传播[J].应用数学和力学，1986,7(7):571-581.
[3]	张善元, 庄蔚.非线性弹性杆中的应变孤波[J].力学学报, 1998,20(1):58-66.
[4]	Makhankov V G.Dynamics of classical soliton(in non-integrable systems)[J].Physics Reports,Phys Lett C,1978,35(1):1-128.
[5]	Liu Y. Existence and blow up of solution of a nonlinear Pochhammer-Cheer equation[J].Indiana Univ Math J,1996,45(3):797-816.
[6]	Akmel Dé Godefrog.Blow up of solutions of a generalized Boussinesq equation[J].IMA Journal of Applied Mathematics,1998,60(1):123-138. doi: 10.1093/imamat/60.2.123
[7]	Liu Y. Strong instability of solitary-waves solutions of a generalized Boussinesq equation[J].J Differential Equations,2000,164(2):223-239. doi: 10.1006/jdeq.2000.3765
[8]	Adrian Constantin,Luc Molinet. The initial value problem for a generalized Boussinesq equation[J].Differential and Integral Equations,2002,15(9):1061-1072.
[9]	CHEN Guo-wang,WANG Shu-bin.Existence and nonexistence of global solution for the generalized IMBq equation[J].Nonlinear Analysis TMA,1999,36(8):961-980. doi: 10.1016/S0362-546X(97)00710-4
[10]	WANG Shu-bin,CHEN Guo-wang.Small amplitude solutions of the generalized IMBq equation[J].J Math Anal,2002,274(2):846-866. doi: 10.1016/S0022-247X(02)00401-8
[11]	CHEN Guo-wang,WANG Shu-bin.Existence and nonexistence of global solution for nonlinear hyperbolic equations of higher order[J].Comment Math Univ Carolin,1995,36(3):475-487.
[12]	CHEN Xiang-ying.Existence and nonexistence of the global solutions for nonlinear evolution equation of fourth-order[J].Appl Math J Chinese Univ Ser B,2001,16(3):251-258. doi: 10.1007/s11766-001-0063-6
[13]	CHEN Xiang-ying,CHEN Guo-wang.Asymptotic behavior and blow-up of solutions to a nonlinear evolution equation of fourth orders[J].Nonlinear Analysis TMA,2008,68(4):892-904. doi: 10.1016/j.na.2006.11.045
[14]	WANG Shu-bin,CHEN Guo-wang. Cauchy problem of the generalized double dispersion equation[J].Nonlinear Analysis TMA,2006,64(1):159-173. doi: 10.1016/j.na.2005.06.017
[15]	Levine H A. Some additional remarks on the nonexistence of global solutions to nonlinear wave equations[J].SIAM J Math Anal,1974,5(1):138-146. doi: 10.1137/0505015
[16]	Liu Y, Xu R.Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation[J].Physica D,2008,237(6):721-731. doi: 10.1016/j.physd.2007.09.028