非齐次Burgers方程解的渐近性行为

C·S·拉奥; M·K·亚达夫

doi:10.3879/j.issn.1000-0887.2010.09.012

非齐次Burgers方程解的渐近性行为

doi: 10.3879/j.issn.1000-0887.2010.09.012

马德拉斯技术学院数学系,钦奈 600036,印度

基金项目: 印度科学和工业研究委员会资助项目(09/84(366)/2005-EMR-I)

详细信息

中图分类号: O175.24
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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-06-04
- 刊出日期: 2010-09-15

Large Time Asymptotics for Solutions of a Nonhomogeneous Burgers Equation

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India

摘要

摘要: 构造了非齐次Burgers方程的解，方程服从有界和紧致的初始曲线，作了一个有趣的探索．将热方程初值问题（L2(R,ex2/2)中有初值）的解，表示为该热方程自相似解的一个级数，Kloosterziel方法立即显示出该初值问题解的渐近性行为．受Kloosterziel方法的启发，根据热方程的自相似解，来表示非齐次Burgers方程的解．最后得到该非齐次Burgers方程解的渐近性特征．
- 非齐次Burgers方程 /
- Hermite多项式 /
- 自相似解
Abstract: Solutions of a nonhomogeneous Burgers equation subject to bounded and compactly supported initial profiles were constructed.In an interesting study,Kloosterziel(Kloosterziel R C.J Engrg Math,1990, 24(3):213-236)represented the solution of an initial value problem(IVP)for the heat equation,with initial data in(L²(R,e^x²/2),as a series of the self-similar solutions of the heat equation.This approach quickly revealed the large time behaviour for the solution of the IVP.Inspired by Kloosterziel's approach, the solution of the nonhomogeneous Burgers equation in terms of the self-similar solutions of the heat equation was expressed.Finally,the large time behaviour of the solutions of the nonhomogeneous Burgers equation is obtained.
- nonhomogeneous Burgers equation /
- Hermite polynomials /
- self-similar solutions

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参考文献(10)

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