带Neumann边界条件的耗散半线性波动方程外问题的生命跨度估计

数学物理学报 ›› 2021, Vol. 41 ›› Issue (4): 1033-1041.

带Neumann边界条件的耗散半线性波动方程外问题的生命跨度估计

赵菁蕾¹(),兰家诚^1,*(),杨姗姗²()

¹ 丽水学院教师教育学院浙江丽水 323000
² 浙江理工大学理学院杭州 310018

收稿日期:2020-05-07 出版日期:2021-08-26 发布日期:2021-08-09
通讯作者: 兰家诚 E-mail:zjl750309@163.com;jiachenglan@163.com;yss960501@163.com
作者简介:赵菁蕾, E-mail: zjl750309@163.com|杨姗姗, E-mail: yss960501@163.com

Lifespan Estimate of Damped Semilinear Wave Equation in Exterior Domain with Neumann Boundary Condition

Jinglei Zhao¹(),Jiacheng Lan^1,*(),Shanshan Yang²()

¹ College of Teacher Education, Lishui University, Zhejiang Lishui 323000
² School of Science, Zhejiang Sci-Tech University, Hangzhou 310018

Received:2020-05-07 Online:2021-08-26 Published:2021-08-09
Contact: Jiacheng Lan E-mail:zjl750309@163.com;jiachenglan@163.com;yss960501@163.com

摘要/Abstract

摘要：

该文讨论了在零Neumann边界条件下耗散半线性波动方程外问题的生命跨度上界估计，并得到了与$\mathbb{R}^n （n\ge 1）$中小初值柯西问题相同的生命跨度上界估计.与文献[6]中相应的结果相比，在二维情形与带零Dirichlet边界条件的外问题具有不同的生命跨度估计，与文献[16]中相应的结果相比，则在一维情形（半直线）与带零Dirichlet边界条件的初边值问题具有不同的临界指标.

关键词: 生命跨度, 耗散半线性波动方程, Neumann边界条件, 外问题

Abstract:

This paper concerns about the upper bound of lifespan estimate to damped semilinear wave equations in exterior domain with vanishing Neumann boundary condition. We find that the initial boundary value problem with Neumann boundary condition admits the same upper bound of lifespan as that of the Cauchy problem in $\mathbb{R}^n (n\ge 1)$. This fact is different from the zero Dirichlet boundary value problem in 2-D exterior domain for lifespan estimate, compared to the corresponding result in ^[6], and is also different from the zero Dirichlet boundary value problem on half line for critical power, compared to the result in ^[16].

Key words: Lifespan, Damped semilinear wave equations, Neumann boundary condition, Exterior problem

中图分类号:

O175.2

赵菁蕾,兰家诚,杨姗姗. 带Neumann边界条件的耗散半线性波动方程外问题的生命跨度估计[J]. 数学物理学报, 2021, 41(4): 1033-1041.

Jinglei Zhao,Jiacheng Lan,Shanshan Yang. Lifespan Estimate of Damped Semilinear Wave Equation in Exterior Domain with Neumann Boundary Condition[J]. Acta mathematica scientia,Series A, 2021, 41(4): 1033-1041.

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