Large-Time Asymptotics for Periodic Solutions of the Modified Burgers Equation

In this paper, we construct large-time asymptotic solution of the modified Burgers equation with sinusoidal initial conditions by using a balancing argument. These asymptotics are validated by a careful numerical study.     

Exact N-Wave Solutions of Generalized Burgers Equations

Exact N-Wave solutions for the generalized Burgers equation where j, α, β, and γ are nonnegative constants and n is a positive integer, are obtained. These solutions are asymptotic to the (linear) old-age solution for large time and extend the validity of the latter so as to cover the entire time regime starting where the originally sharp shock has become sufficiently thick and the viscous effects are felt in the entire N wave.     

Large-Time Behavior of Periodic Solutions to Fractal Burgers Equation with Large Initial Data

The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutio...     

Large Time Asymptotic Behaviors for Periodic Solutions of Generalized Burgers Equations With Spherical Symmetry or Linear Damping

Using the method of balancing arguments, large time asymptotic behaviors for the periodic solutions of generalized Burgers equations   u_t  +  u ³ u_x  +  ju /2 t  =δ/2 u_xx   and   u_t  +  u ³ u_x  +λ u  =δ/2 u_xx   subject to the periodic initial condition     and the vanishing boundary conditions   u (0,  t ) =  u ( l ,  t ) = 0,   t  ≥ 0   or    t ₀,  where   A ,  A ₁, δ, λ,  l ,  t ₀, ∈ R ⁺  and   j  = 1, 2  , are obtained.     

一类延迟积分方程的渐近概周期解

积分方程解的性态是积分理论中一个重要而又基本的问题.其中关于方程的周期解、概周期型解的存在性问题更是具有重要的理论意义和应用价值.已有文献中,有的延迟是常数,而有的延迟虽为函数,但对延迟做了是概周期函数的假设.本文在某些延迟积分方程的概周期解的存在性的基础上,并利用渐近概周期函数的定义和不动点理论,讨论了一类延迟是渐近概周期函数的积分方程的渐近概周期解的存在性.     

Generalized Burgers Equations Transformable to the Burgers Equation

Using the mappings which involve first‐order derivatives, the Burgers equation with linear damping and variable viscosity is linearized to several parabolic equations including the heat equation, by applying a method which is a combination of Lie’s classical method and Kawamota’s method. The independent variables of the linearized equations are not t, x but z(x, t), τ(t) , where z is the similarity variable. The linearization is possible only when the viscosity Δ(t) depends on the damping parameter α and decays exponentially for large t . And the linearization makes it possible to pose initial and/or boundary value problems for the Burgers equation with linear damping and exponentially decaying viscosity. Bäcklund transformations for the nonplanar Burgers equation with algebraically decaying viscosity are also reported.     

非齐次Burgers方程解的渐近性行为

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[Kloosterziel RC.J Engrg Math,1990,24(3):213-236],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.     

具有偏差变元的广义二阶Rayleigh型中立微分方程的周期解

研究了一类具有多个偏差变元的广义二阶Rayleigh型中立微分方程的周期解.通过利用重合度理论和不等式分析技巧,获得了方程周期解存在性新的充分条件,推广和改进了早期文献的相关结果.最后,给出一个例子,说明所得结果的可行性.     

广义KdV方程与广义Burgers方程的精确解

利用试探函数法和直接积分法构造广义KdV方程与广义Burgers方程的新的精确解.     

一类一阶和二阶微分方程的渐近概周期解

对于一阶微分系统u′+F(u)=h(t),其中F为R~n上的严格单调算子,本文给出了其渐近概周期解存在和唯一的一个充分条件和一个必要条件.特别,对于一阶微分系统u′+▽Φ(u)=h(t),其中▽Φ代表R~N上凸函数Φ的梯度,讨论了其渐近概周期解存在和唯一的充分必要条件,并且把一些结果推广到了一类二阶方程.     

一类积分方程的向量值遥远概周期解

讨论了向量值遥远概周期函数空间上一类积分算子的不变性,并应用此结果对一类积分方程的向量值遥远概周期解的存在唯一性进行了研究,得到了其遥远概周期解存在唯一的一个充分性条件.     

具多偏差变元的n-维p-Laplacian方程周期解的存在性

研究了一类具多偏差变元的n-维p-Laplacian方程周期解的存在性,利用迭合度理论得到了存在周期解的新条件.     

一类Burgers方程的孤立波解

Burgers方程在工程上有着重要的应用,它可以用来描述湍流、车队的交通流、氏族的随机迁移、化学工程中的分离等现象,对Burgers方程求解方法的研究有着重要的现实意义.对Burgers方程求解主要是应用差分和微分两方面的方法来展开求解的,1/G展开法是近年来发展起来的求解非线性偏微分方程的一种较为有效的微分解法.采用...     

Similarity Solutions of a Generalized Burgers Equation

The similarity method is applied to a generalized Burgers equationwhich has been applied to shock waves and to sound waves. Threedifferent cases of the equation, each allowing a three-parametersymmetry group, are found. The corresponding reduction to anordinary differential equation is given. The Lie algebras ofthe groups are identified with standard types given by Bianchi.     

多滞量二阶中立型方程的周期解

本文利用Fourier级数理论,讨论了一类多滞量二阶中立型方程的周期解问题,获得了若干确保周期解存在唯一的充分条件,并推广、改进和完善了一些相关文献的结果．     

Periodic Solutions for Nonlinear Diferential Equations

ＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｆｏｒＮｏｎｌｉｎｅａｒＤｉｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓＣｏｎｇＦｕｚｈｏｎｇ（从福仲）（ＯｆｆｉｃｅｏｆＭａｔｈｅｍａｔｉｃｓ，８６００３Ｕｎｉｔ，Ｃｈａｎｇｃｈｕｎ，１３００２２）ＭａｏＤｏｎｇｍｉｎｇ（...     

一类广义耦合的非线性波动方程组时间周期解的存在性

研究了一类广义耦合的非线性波动方程组关于时间周期解的问题.首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Laray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.     

关于“广义Liénard方程的周期解”一文的注记

本文研究广义Ｌｉéｎａｒｄ方程x+f(x,x)x+g(x)=0的周期解的存在性，所得结果不仅较大地改进了文［１］的定理而且还指出了文［１］中的错误。     

一类广义Liénard方程的概周期解

研究广义 Liénard方程: x'=φ(y)-F(x), y'=-g(x)+p(t), 利用 Amerio的结果证明方程的解部分变元的最终有界性意味着概周期解的存在性, 推广了Cieutat^[1]的主要结果.