摘要
考虑了定义在一个半无穷柱体上伪抛物方程的渐近性质,其中在柱体的有限端施加了的非线性边界条件.首先定义了一个能量表达式,并得到了关于此能量表达式的二阶微分不等式.通过对三种不同类型的无界区域进行分析,运用微分不等式技术和能量估计的方法,得到了伪抛物方程的Phragmén-Lindelof二择一结果.在衰减的情形,推导了全能量的显式上界.
In this paper,we consider the asymptotic properties of the pseudo parabolic equation defined on a semi infinite cylinder,in which the nonlinear boundary conditions are imposed on the finite end of the cylinder.Firstly,we define an energy expression and obtain the second order differential inequality about the energy expression.By analyzing three different types of unbounded regions,we use the differential inequality technology and the method of energy estimation to obtain an alternative result of Phragmén-Lindelof results for the pseudo parabolic equation.In the case of decay,the explicit upper bound of total energy is derived.
作者
李远飞
张旖
LI Yuan-fei;ZHANG Yi(Huashang College Guangdong University of Finance&Economics,Guangzhou 511300,China)
出处
《数学的实践与认识》
北大核心
2020年第12期220-232,共13页
Mathematics in Practice and Theory
基金
广东省普通高校重点项目(自然科学)(2019KZDXM042)
广东省自然科学基金(2017A030313037)
广州市科技创新一般项目(2017070710126)。
关键词
伪抛物方程
二择一
能量估计
pseudo-parabolic equations
Phragmén-Lindelof alternative
energy estimates
