The Study of Solution to the Generalized Hyperelasticrod Equation 

Author  ShiMin 
Tutor  DingDanPing 
School  Jiangsu University 
Course  Applied Mathematics 
Keywords  the generalized hyperelasticrod equation the initial boundary problem global solution Blowup global exponential stability global asymptotic stability 
CLC  O175.29 
Type  Master's thesis 
Year  2008 
Downloads  9 
Quotes  0 
In this paper,we study the Cauchy problem of the existence of the local solution,the Blowup of solution for the generalized hyperelastic rod equation,and the characters of it’s solution to initial boundary problem,There are three sections in this paper:The first section,we will introduce the background and actuality and summerize the main results.The second section,we consider the Cauchy problem of the generali zed hyperelasticrod equation,with Kato’s method for abstract quasilinear evolution equations and a prior estimates,we get the existence of the local solution,the Blowup of solution and it’s exact blowup rate.Finally,we consider the initial boundary problem of the generalized hyperelasticrod equation,the existence of global solution,H~1 global exponential stability and H~2 global asymptotic stability are obtained in this section.