具有记忆项的对数 Boussinesq型方程解的长时间行为研究
Study on the Longtime Behavior of the Solution of Logarithmic Boussinesq Type Equations with Memory
DOI: 10.12677/PM.2023.1311343, PDF, 下载: 79  浏览: 141 
作者: 王爽, 闫龙:东北电力大学理学院,吉林 吉林
关键词: 对数梁方程记忆项整体存在性指数增长能量衰减Logarithmic Beam Equations Memory Global Existence Exponential Growth Energy Decay
摘要: 本文考虑一类具有记忆项的对数梁方程的初边值问题。利用 Galerkin 方法结合对数 Sobolev 不等式及对数 Gronwall 不等式,我们证明了解的全局存在性。在此基础上,我们借助位势井思想进一步得到了系统在适当初值条件下的指数烹减及指数增长。
Abstract: This paper is concerned with the initial value problem of a logarithmic beam equations with memory. Using Galerkin method, logarithmic Sobolev inequality and the Gronwall inequality, we obtain the global existence of the solutions. Moreover, we prove the exponential decay and exponential growth of the system by using potential well theory.
文章引用:王爽, 闫龙. 具有记忆项的对数 Boussinesq型方程解的长时间行为研究[J]. 理论数学, 2023, 13(11): 3295-3315. https://doi.org/10.12677/PM.2023.1311343

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