一类具有对数非线性项的四阶抛物型方程解的全局渐近性
Global Asymptotic Behavior of Solutions for a Class of Fourth-Order Logarithmic Nonlinear Parabolic Equations
DOI: 10.12677/AAM.2020.911236, PDF, HTML, XML, 下载: 640  浏览: 1,517 
作者: 彭 迪, 石 鹏：贵州民族大学，数据与信息工程学院，贵州 贵阳
关键词: 四阶抛物型方程；指数衰退；爆破时间；对数非线性；Fourth Order Parabolic Equation； Exponential Decay； Blow-Up Time； Logarithmic Nonlinearity
摘要: 本文研究了一类具有对数非线性项的四阶抛物型方程的初值问题。通过运用势阱法及构造相应的能量泛函，证明了低初始能量条件下方程解的渐近性和爆破性，并给出了爆破时间的下界估计。
Abstract: In this paper, the initial value problem for a class of fourth-order parabolic equations with logarithmic nonlinear terms is studied. By applying the potential well method and constructing the corresponding energy general function, the asymptotic and bursting properties of the solutions are proved for low initial capacities, and lower bound estimates of the bursting time are given.
文章引用：彭迪, 石鹏. 一类具有对数非线性项的四阶抛物型方程解的全局渐近性[J]. 应用数学进展, 2020, 9(11): 2036-2045. https://doi.org/10.12677/AAM.2020.911236

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