半线性波动方程Cauchy问题解的生命跨度估计

Lifespan Estimation of Solutions to Cauchy Problem of Semilinear Wave Equation

该文研究了Rn中半线性波动方程utt-Δu=(1+|x|2)α|u|p的小初值Cauchy问题解的生命跨度估计.主要利用了改进的Kato型引理,得到了当n=2,1 <p≤2时及n=1,p> 1时改进的生命跨度上界估计.

In this paper,the lifespan estimate to the Cauchy problem of the semi-linear wave equation utt-△u=(1+|x|2)α|u|p in Rn is studied.The upper bound of lifespan is improved for the cases n=2,1<p≤2 and n=1,p> 1,by using the improved Kato’s type lemma.