带位势项的非线性波动方程解的大时间行为与空间维数、非线性项的指数有着密切的联系.当非线性项的指数与空间维数满足一定关系时,将证明小初值Cauchy问题的解在有限时间内破裂.进一步,将建立解的生命跨度上界估计.%The long-time behavior of the solutions to nonlinear wave equations with potential largely dependson the dimension and the power of the nonlinear term. In this paper,we establish the blow-up result of thesmall data Cauchy problem of nonlinear wave equations with potential,assuming that the exponent of thenonlinear term satisfies some condition. Furthermore,we obtain the upper bound of the life span.
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