具有输入输出的非线性波动方程的爆破解  

Blow-Up Solutions for a Nonlinear Wave Equation with Input and Output

作　　者：李海燕 武洁琼[2] 

机构地区：[1]阳泉师范高等专科学校数学系,山西阳泉045200 [2]山西大学数学科学学院,山西太原030006

出　　处：《中北大学学报（自然科学版）》2013年第5期537-539,共3页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学(青年)基金资助项目(61104129);山西省自然科学(青年)基金资助项目(2011021002-1)

摘　　要：研究了边界具有输入输出结构的非线性弦振动方程的解的爆破问题.利用能量方法分析了边界输入输出结构和内部非线性源项的相互作用.引入适当的辅助函数,通过分析该辅助函数的导函数的性质,得到了它爆破的充分条件.进而得到了结论:假设系统的初始能量非正,初值函数、输入函数和输出函数满足适当的条件,系统的解就在有限时刻爆破.The blow-up problem of the solutions for the nonlinear string equation with boundary input-output structure was studied. The interaction between boundary input-output structure and interior nonlinear source term was analyzed by using energy method. An auxiliary function was introduced. And according to the prop- erties of the derivative of the auxiliary function, the sufficient conditions under which the auxiliary function blew up were obtained. Thus it draws the conclusion that the solutions of the system blow up in finite time if the initial energy of the system is non-positive and the input and output functions satisfy some conditions.

关 键 词：弦振动方程 非线性源项 边界输入输出 爆破解 

分 类 号：O175.4[理学—数学]