Lifespan estimates for 2-dimensional semilinear wave equations in asymptotically Euclidean exterior domains
Lifespan estimates for 2-dimensional semilinear wave equations in asymptotically Euclidean exterior domains
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DOI：
10.1016/j.jfa.2021.109253
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发表时间：
2020-06
影响因子：
1.7
通讯作者：
Ning-An Lai;Mengyun Liu;Kyouhei Wakasa;Chengbo Wang
中科院分区：
文献类型：
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作者：
Ning-An Lai;Mengyun Liu;Kyouhei Wakasa;Chengbo Wang
本文研究了在渐近欧几里得外域上具有小数据的二维半线性波动方程的初边值问题。证明了当1< p≤p c(2)时，该问题的寿命上界与对应的柯西问题几乎相同，只是在1< p≤2时损失较小。有趣的是，2- d中谐波函数的对数增长对2< p≤p c(2)的寿命上界的估计没有影响。新颖之处在于，我们可以处理平面度规和一般障碍（有界和单连通）的问题，并将其简化为球外平面度规的紧致摄动的相应问题。
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≤ 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≤ 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≤ p c (2). One of the novelties is that we can deal with the problem with flat metric and general obstacles (bounded and simply connected), and it will be reduced to the corresponding problem with compact perturbation of the flat metric outside a ball.