具有阻尼项的高阶波动方程整体解的不存在性

利用试验函数方法研究了带有线性阻尼项ut和非线性阻尼项(g(u))t的2类高阶波动方程的初值问题非平凡整体解的不存在性.结果表明:当初值函数满足一定的条件时,第1类方程的任何非平凡整体解必在有限时间内爆破;当参数和指数满足一定的条件时,第2类方程也不存在非平凡整体解.

Nonexistence of global solution to higher-order wave equation with damping term

By use of the test function method,the nonexistence of nontrivial global solution to the initial-value problem of 2 kinds of higher-order wave equations,one with a linear damping term ut and the other with a nonlinear damping term(g(u))t,was discussed.The result shows that,if the initial-value function meets a certain condition,any nontrivial global solution to the first kind of equations is sure to blow up within a certain period of time,while if the parameters and indexes satisfy a certain condition,nontrivial global solution to the second kind of equations also does not exist.