一类弹性杆的振动问题解的整体存在性  

Global Solutions to a Vibration Systemic of Elastic Rod

作　　者：裴金仙[1] 

机构地区：[1]山西大学商务学院,山西太原030031

出　　处：《中北大学学报（自然科学版）》2013年第5期567-569,共3页Journal of North University of China(Natural Science Edition)

摘　　要：研究了一类具有阻尼项和源项的弹性杆振动系统的初边值问题,这类问题源于物理学中弹性杆的纵向振动.利用偏微分方程理论和能量扰动法,通过构造辅助函数和微分不等式,给出了对一定的初值,当阻尼项和源项的增长阶数满足一定条件时,系统的解是整体存在的.给出了解整体存在的条件是充分条件.研究结果是部分文献结果的推广.The initial boundary value problem of a elastic rod vibration system with damping and source term was studied. This problem came from the vertical vibration of a elastic rod in physics. By the theory of partial differential equation and the energy perturbation method, and by constructing auxiliary functions and differen- tial inequality, it is proved the solutions are global under some conditions on growth orders of the damping and the source term. The conditions are sufficient. The results are of the promotion of part literature.

关 键 词：弹性杆 振动问题 能量扰动法 解的整体存在性 

分 类 号：O175.29[理学—数学]