Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation

被引：5
|
作者：
Zuparic, Mathew [1 ]
Hoek, Keeley [2 ]
机构：
[1] Def Sci & Technol Grp, Canberra, ACT 2600, Australia
[2] Australian Natl Univ, Canberra, ACT 2601, Australia
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2019年 / 73卷
关键词：
Burgers hierarchy; Forced Burgers; Generalized hypergeometric function; Higer order heat type equation; Fokker-Planck; PAINLEVE PROPERTY; LINEARIZATION; STABILITY; MODEL;
D O I：
10.1016/j.cnsns.2019.01.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Green's function of the corresponding linear equation of arbitrary order N is shown to be a sum of generalised hypergeometric functions. For suitably damped initial conditions we plot the time dependence of the Cauchy problem over a range of N values. For N = 1, we introduce a spatial forcing term. Using connections between the associated second order linear Schrodinger and Fokker-Planck equations, we give closed form expressions for the corresponding Green's functions of the sinked Bessel process with constant drift. We then apply the Green's function to give time dependent profiles for the corresponding forced Burgers Cauchy problem. Crown Copyright (c) 2019 Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：275 / 290
页数：16
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