二维空间上一类半线性波动方程的爆破问题

Blow-up for the semilinear wave Equations in Two-dimensional Space

本文用类似于[1]中解决爆破问题的方法，对二维空间上一类半线性波动方程的初值问题证得了：当非线性项F（u）∈C2（R）和初值g（x）∈CO（R2）且满足一定条件时，初值问题不存在全局C2-解．

In this paper, we use the method similar to that used by [1] to deal with theblow-up of soluitions to the initial value problem for a semi-linear wave equations andobtain a theorem: suppose that the non-linear term F(u) ∈ C2(R) and the initial valuefunction g (x) ∈ C2 (R2) and they satisy certain conditions, then there is no global classicalsolutions for the initial value problem.