N维外区域中带变系数非线性项的半线性波动方程解的爆破  

Blow up of Solutions to Semilinear Wave Equations with Variable Coefficient for Nonlinearity in an N-Dimensional Exterior Domain

作　　者：黄守军 王娟 Huang Shoujun;Wang Juan(School of Mathematics and Statistics,Anhui Normal University,Anhui Wuhu 241002)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《数学物理学报（A辑）》2020年第5期1259-1268,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(11301006,11871075);安徽省自然科学基金(1408085MA01)。

摘　　要：该文考虑N(N≥2)维外区域中一类具有变系数非线性项的半线性波动方程的外问题,主要研究解的爆破和生命估计.基于文献[19-20]的方法,利用N=2及N≥3时外区域满足Dirichlet边界条件的调和函数以及测试函数方法,求出上述外问题解的生命跨度.特别地,变系数对解的的生命跨度的影响也在文中详细讨论.In this paper,we are concerned with the N(N≥2)-dimensional exterior problem for a class of semilinear wave equations with variable coefficient nonlinearity.We mainly consider the blow up and lifespan of the solutions.Base on[19-20],by utilizing the test function and the harmonic functions of N=2 and N≥3 in the exterior domains with Dirichlet boundary condition,we are able to derive the upper bound of lifespan.In particular,the impact of the variable coefficient nonlinearity on the lifespan has been discussed in detail.

关 键 词：半线性波动方程 外区域 爆破 生命估计 

分 类 号：O175.2[理学—数学]