| 一类具有超线性源项四阶双曲方程解的存在性及爆破时间估计 |
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| 引用本文： | 廖祥永,高艳超.一类具有超线性源项四阶双曲方程解的存在性及爆破时间估计[J].吉林大学学报(理学版),2021,59(3):551-554. |
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| 作者姓名： | 廖祥永 高艳超 |
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| 作者单位： | 长春理工大学 理学院, 长春 130022 |
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| 摘 要： | 先用Galerkin逼近和位势井方法证明一类具有超线性源项的四阶双曲方程初边值问题在小初值时解的全局存在性; 再在初始能量为负时, 利用Levine凸方法证明其解在有限时刻爆破.
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| 关 键 词： | 超线性源项 四阶双曲方程 整体解 爆破 |
| 收稿时间： | 2021-01-26 |
Existence and Blow up Time Estimates of Solution for a Class of Fourth Order Hyperbolic Equations with Superlinear Source Terms |
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| LIAO Xiangyong,GAO Yanchao.Existence and Blow up Time Estimates of Solution for a Class of Fourth Order Hyperbolic Equations with Superlinear Source Terms[J].Journal of Jilin University: Sci Ed,2021,59(3):551-554. |
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| Authors: | LIAO Xiangyong GAO Yanchao |
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| Institution: | School of Science, Changchun University of Science and Technology, Changchun 130022, China |
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| Abstract: | We first used Galerkin approximation and potential well method to prove the global existence of the solution for a class of fourth order hyperbolic equations with superlinear source terms at small initial values, and then we proved the solution blew up at finite time by using Levine convex method when the initial energy was negative. |
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| Keywords: | superlinear source term fourth order hyperbolic equation global solution blow up |
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