渐近欧氏流形上带有阻尼和位势项的波动方程的生命跨度估计  

Lifespan Estimates for Wave Equations with Damping and Potential Posed on Asymptotically Euclidean Manifolds

作　　者：刘梦云 LIU Mengyun(Department of Mathematics,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学数学系,杭州310018

出　　处：《数学年刊（A辑）》2022年第3期251-262,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.12101558,No.11971428);浙江省自然科学基金(No.LQ22A010016)的资助。

摘　　要：本文研究了渐近欧氏流形上带有阻尼和位势的半线性波动方程的有限时间破裂以及解的生命跨度上界估计,其半线性项是形如c_(1)|u_(t)|^(p)+c_(2)|u|^(q)的混合项.该问题与Strauss猜测和Glassey猜测紧密相关.In this work,the author investigates the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with time dependent damping and potential,and mixed nonlinearities c_(1)|u_(t)|^(p)+c_(2)|u|^(q),posed on asymptotically Euclidean manifolds,whichc is related to both the Strauss conjecture and the Glassey conjecture.

关 键 词：破裂 生命跨度估计 渐近欧氏流形 阻尼 位势 

分 类 号：O175.29[理学—数学]