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  

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

作　　者：赵菁蕾[1] 兰家诚 杨姗姗 Zhao Jinglei;Lan Jiacheng;Yang Shanshan(College of Teacher Education,Lishui University,Zhejiang Lishui 323000;School of Science,Zhejiang Sci-Tech University,Hangzhou 310018)

机构地区：[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

出　　处：《数学物理学报（A辑）》2021年第4期1033-1041,共9页Acta Mathematica Scientia

摘　　要：该文讨论了在零N eumann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R^(n)(n≥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.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 R^(n)(n>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].

关 键 词：生命跨度 耗散半线性波动方程 NEUMANN边界条件 外问题 

分 类 号：O175.2[理学—数学]