一类强阻尼非线性波动方程解的blow up

blow up of Solutions for a Class of Strongly Nonlinear Wave Equations

考虑了模拟粘弹性杆中纵波振动的一类强阻尼非线性波动方程utt=αuxxt+σ(ux) x- f(u)的初边值问题解的非存在性和blowup问题 .利用能量估计方法和特征函数方法 ,证明了在非线性函数σ(s) ,f(s)的某些假设下 ,初边值问题的解在有限时间内blowup 。

This paper considers global nonexistence and blow up of solutions of the initial boundary value problems for a class of strongly damped nonlinear wave equations modeling the longitudinal vibration of a viscous elastic bar. It has been proved that the solutions of the problem blow up in finite time under certain conditions on nonlinear functions σ(s), f(s) and the initial data by using energy estimate method and eigenfunction method. The results in this paper have improved and generalized some known results.