摘要
本文讨论用Green函数方法研究非线性发展方程初值问题解的大时间状态的逐点估计.在简要介绍Green函数的基本思想后,本文通过两个例子说明,对带耗散和双曲结构的非线性发展方程,其相应初值问题的解在双曲机制、抛物机制和非线性机制作用下,如何通过Green函数的方法厘清各种机制的作用,清晰看到其精细结构,并解释其他方法难以解释的一些令人诧异的现象.
This paper studies pointwise estimates of solutions to initial value problems of large time behavior of nonlinear evolution equations in small perturbation cases by using the Green function method.Introducing the basic idea of Green function,this paper will exemplify under hyperbolic,parabolic and nonlinear mechanisms,how Green function helps the solutions to initial value problems of dissipative and hyperbolic structured nonlinear evolution equations sort out various mechanisms,find out fine structures,and figure out some amazing phenomena with which other methods could not deliver a clear explanation.
出处
《中国科学：数学》
CSCD
北大核心
2019年第2期249-266,共18页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11771284)资助项目
关键词
逐点估计
双曲机制
一般Huygens原理
阻尼机制
衰减率
pointwise estimate
hyperbolic mechanism
generalized Huygens’ principle
damping mechanism
decay rate
