半线性波动方程在三维空间中解的破裂和生命跨度的上界估计

Blow-Up of Solutions and Estimate the Upper Bound of Life Span for Semilinear Wave Equation in Three-Dimensional Space

运用试探函数法研究了三维空间中半线性波动方程在外区域上的初边值问题,得到结论:不论初值多么小,解总会在有限时间内破裂,得到了解的生命跨度的上界估计,并且找到了试探函数Φ0(x)的显式表达式.

The initial boundary value problem for semilinear wave equation on exterior domain in 3-D was studied by using test function method.The results show that blow up of solutions and the upper bound of life span estimate are established,no matter how small the data are.And the explicit expression the test function Φ_0（x）is founded.