一类系数依赖于时间的非线性项的半线性双波动方程解的爆破研究

Blow-up Study on Semi-linear Double-Wave Equation with Time-Dependent Coefficient on Nonlinearity

考虑了一类系数依赖于时间的非线性项的半线性双波动方程解的爆破情况.运用微分不等式方法和迭代方法证明了在次临界情况下半线性双波动方程柯西问题的解在有限时间内爆破,且给出了生命跨度的上界估计.进一步推广了波动方程在高阶上柯西问题的有关结果.

In this paper,the blow-up of solutions has been considered to a class of semi-linear double-wave equations with time-dependent coefficient on the nonlinearity.By means of differential inequalities and an iteration argument,the blow-up and the upper bound of the lifespan of solutions have been obtained to the Cauchy problem for semi-linear double-wave equations in the subcritical case,which generalize further the facts on the Cauchy problem for wave equations in high orders.