具正初始能量的耦合波动方程解的整体不存在

Global Nonexistence of Solution to Coupled Wave Equations with Positive Initial Energy

下载PDF

导出

摘要考虑带有非线性阻尼和源项的耦合黏弹性波动方程的初边值问题.假设系统具有正初始能量,在适当的条件下证明了解的整体不存在性定理. Consider the initial-boundary problem for a coupled system of viscoelastic wave equations with nonlinear damping and source terms.Under some suitable assumptions,the theorem of global nonexistence is proved,provided that the initial energy of the system is positive.

作者武洁琼李胜家

机构地区山西大学数学科学学院山西大学数学与应用数学研究所

出处《应用泛函分析学报》 CSCD 2012年第2期199-205,共7页 Acta Analysis Functionalis Applicata

基金国家自然科学基金(60774014)

关键词非线性波动方程正初始能量整体不存在性 nonlinear wave equations positive initial energy global nonexistence

分类号 O175.9 [理学—基础数学]

引文网络
相关文献

参考文献10

1Levine H A. Some additional remarks on the nonexistence of global solutions to nonlinear wave equa?tions[J]. SIAM J Math Anal. 1974, 5(4): 138-146.
2Levine H A. Instability and nonexistence of global solutions of nonlinear wave equation of the form PUtt = -Au + F(u)[J]. Trans Arner Math Soc 1974, 192: 1-21.
3Georgiev V, Todorova G. Existence of solution of the wave equation with nonlinear damping and source term[J]. J Differential Equation, 1994, 109: 295-308.
4Messaoudi S A. Blow-up in a nonlinearly damped wave equation[J]. Math Nachy 2001, 231: 1-7.
5Vitillaro E., Global nonexistence theorem for a class of evolution equations with dissipation[J]. Arch Ration Mech Anal, 1999, 149: 155-182.
6HAO Jianghao, ZHANG Yajing, Li Shengjia, Global existence and blow-up phenomena for a nonlinear wave equation[J]. Nonlinear Analysis, 2009, 71(10): 4823-4832.
7Salim A. Messaoudi, Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation[J]. J Math Anal Appl, 2006, 320: 902-915.
8Agre K, Rammaha M A. System of nonlinear wave equations with damping and source terms[J). Differ?ential Integral Equations, 2006, 19: 1235-1270.
9HAN Xiaosen, WANG Mingxin. Global existence and blow-up of solution for a system of nonlinear viscoelastic wave equations with damping and source[J). Nonlinear Analysis, 2009, 70(9): 3264-3272.
10WU Jieqiong, LI Shengjia, CHAI Shugen. Existence and nonexistence of a global solution for coupled nonlinear wave equations with damping and source[J]. Nonlinear Analysis (TMA), 2010, 72(11): 3969- 3975.

1孟会会,郝美艳,王晓红.耦合波动方程组解的整体不存在性[J].太原师范学院学报（自然科学版）,2012,11(3):8-11.
2修宗湖,曹秀梅,潘朋波,单海燕.一类非线性反应扩散系统弱解的整体不存在性[J].数学的实践与认识,2007,37(5):125-128.
3张宏伟,呼青英.一类非线性双曲方程整体弱解的存在性和不存在性[J].工程数学学报,2003,20(3):131-134. 被引量：12
4杨静.一类拟线性梁方程振动问题整体解的不存在性[J].长治学院学报,2015,32(5):58-60.
5严永仙,李小梅.含弱阻尼和源项的非线性波方程的初边值问题[J].中国科学技术大学学报,2006,36(7):740-742.
6裴金仙.一类非线性耦合波动方程组解的整体不存在性[J].中北大学学报（自然科学版）,2015,36(5):511-514.
7张宏伟,张桂霞,呼青英.一类多重非线性抛物方程组解的整体不存在性[J].应用泛函分析学报,2016,18(2):204-211.
8张媛媛,赵科.一类四阶非线性发展方程解的整体不存在性[J].科技信息,2009(21).
9邵为爽.具有多个非线性源项与临界初始状态的半线性波动方程的初边值问题[J].科技通报,2013,29(1):9-11. 被引量：1
10王书彬,王秀梅.取油管振动方程解的整体不存在性[J].数学的实践与认识,2007,37(9):69-73.

应用泛函分析学报

2012年第2期

浏览历史

内容加载中请稍等...

具正初始能量的耦合波动方程解的整体不存在

参考文献10

相关作者

相关机构

相关主题

浏览历史