论文标题
在渐近的欧几里得外部域中，$ 2 $维的半维半线性波方程的寿命估计值
Lifespan estimates for $2$-dimensional semilinear wave equations in asymptotically Euclidean exterior domains
论文作者
论文摘要
在本文中，我们研究了在渐近的欧几里得外部结构域中使用小数据的二维半线性波方程的初始边界值问题。我们证明，如果$ 1 <p \ le p_c（2）$，该问题承认了寿命的上限几乎与相应的考奇问题的上限相同，只有$ 1 <p \ le 2 $的小损失。有趣的是，以$ 2 $ -D的谐波功能的对数增加对寿命上限的估计没有影响，价格为$ 2 <p \ le p_c（2）$。新事物之一是，我们可以用平坦的公制和一般障碍物（有限和简单连接）来处理问题，并且它将减少到相应的问题，即紧凑的球外球外的平坦度量。
In this paper we study the initial boundary value problem for two-dimensional semilinear wave equations with small data, in asymptotically Euclidean exterior domains. We prove that if $1<p\le p_c(2)$, the problem admits almost the same upper bound of the lifespan as that of the corresponding Cauchy problem, only with a small loss for $1<p\le 2$. It is interesting to see that the logarithmic increase of the harmonic function in $2$-D has no influence to the estimate of the upper bound of the lifespan for $2<p\le p_c(2)$. One of the novelties is that we can deal with the problem with flat metric and general obstacles (bounded and simple connected), and it will be reduced to the corresponding problem with compact perturbation of the flat metric outside a ball.
