中文摘要：

主要研究了在n（n≥1）维空间下，半线性波动方程在次临界情形时的柯西问题，通过构造一个测试函数ψ（x，t）证明不论正初值多么小，其解都会在有限时间内破裂，并给出其解的生命跨度上界估计．

英文摘要：

This paper is devoted to studying Cauchy problems for semilinear wave equations with subcritical exponents for n（n ≥ 1） space dimensions. By constructing a test functions ψ（x, t）, we prove that solutions cannot be global if the initial values are positive somewhere and nonnegative no matter how small the initial data are, and also we give the upper bound estimate of lifespan of solutions for the problems.