| 刘梦云.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*[J].数学年刊A辑,2022,43(3):251~262 |
| 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* |
| Lifespan Estimates for Wave Equations with Damping and Potential Posed on Asymptotically Euclidean Manifolds |
| Received:May 10, 2021 Revised:January 05, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0017 |
| 中文关键词: 破裂, 生命跨度估计, 渐近欧氏流形, 阻尼, 位势 |
| 英文关键词:Blow up, Lifespan estimates, Asymptotically Euclidean manifolds,Damping, Potential |
| 基金项目:国家自然科学基金 (No.12101558, No.11971428)和浙江省自然科学基金(No.LQ22A010016) |
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| 中文摘要: |
| 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c1 |ut|p + c2 |u|p的混合项. 该问题与Strauss猜测和Glassey猜测紧密相关. |
| 英文摘要: |
| 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 c1 |ut|p + c2 |u|p, posed on asymptotically Euclidean manifolds, whichc is related to both the Strauss conjecture and the Glassey conjecture. |
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