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1.
P. L. Sachdev B. O. Enflo Ch. Srinivasa Rao B. Mayil Vaganan Poonam Goyal 《Studies in Applied Mathematics》2003,110(2):181-204
In this paper, we construct large-time asymptotic solutions of some generalized Burgers equations with periodic initial conditions by using a balancing argument. These asymptotics are validated by a careful numerical study. We also show that our asymptotic results agree with the approximate solutions obtained by Parker [1] in certain limits. 相似文献
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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. 相似文献
3.
We consider perturbed linear systems of difference equations with periodic coefficients. The zero solution of a nonperturbed system is assumed asymptotically stable, i.e., all eigenvalues of the monodromy matrix belong to the unit disk {||<1}. We obtain conditions on the perturbation of this system under which the zero solution of the system is asymptotically stable and also establish continuous dependence of one class of numeric characteristics of asymptotic stability of solutions on the coefficients of the system. 相似文献
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Siberian Mathematical Journal - 相似文献
5.
Using a degree-theoretic result of Granas, a homotopy is constructed enabling us to show that if there is an a priori bound on all possible T-periodic solutions of a Volterra equation, then there is a T-periodic solution. The a priori bound is established by means of a Liapunov functional. The latter result is unusual in that no bounds on the Liapunov functional are required. Thus, in addition to the periodic solution, the equation may have both bounded and unbounded Solutions. 相似文献
6.
We find the form of all subnormal solutions of equation (1.4). Our results generalize and improve a well-known result of Wittich about equation (1.1). Several examples are given. Higher order equations are discussed. 相似文献
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The generalized Burgers equation with linear damping and variable viscosity is subjected to Lie's classical method. Five distinct expressions for the variable viscosity are identified. Both the reduced ordinary differential equations and their corresponding Euler-Painlevé transcendents admit first integrals in the form of Bernoulli's equation and are linearized to obtain solutions in closed form. 相似文献
8.
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. 相似文献
9.
In this paper, we construct spherically symmetric solutions of the equations of compressible flow, which are important in the theory of explosion waves in air, water, and other media. Following McVittie [ 1 ], we write a general solution form, in terms of velocity potential, as a product of a function of time and a function of a similarity variable. First, we find solutions to the equations of motion and continuity without reference to adiabatic or isentropic relation. These solutions are quite general and can be applied to nonadiabatic motions, such as the motions of interstellar gas clouds that lose energy by radiation. All the solutions found by McVittie [ 1 ] have linear velocity profile with respect to distance. We introduce a nonlinear form of the velocity function containing an arbitrary function of the similarity variable. Adiabatic conditions lead to a second-order ODE, which we discuss in some detail. We relate our work to the earlier investigations of Taylor [ 2 ], McVittie [ 1 ], and Keller [ 3 ]. 相似文献
10.
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. 相似文献
11.
Explicit almost periodic solutions are obtained for a class of almost periodic linear difference equations. The stability characteristics of the almost periodic solution are investigated. The results are applied to a nonautonomous hyperbolic difference equation modelling the dynamics of a single species population in temporally varying environments. 相似文献
12.
周期线性微分方程某解f(z)和f(z qω)的线性相关性是方程复振研究的起步关键,其中ω是方程系数的周期,q是某正整数。S.Bank和J.Langley于1992年证明了重要结果,但其优势条件有时不适用。本文提出“组合优势条件”产用其发展了这一结果,大大扩充了其适用性。 相似文献
13.
We construct asymptotic solutions of a singularly perturbed system of integro-differential equations in which the matrix coefficient of the derivative is degenerate at a point. 相似文献
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In this paper, we apply a new procedure initially developed in Refs. [H. El-Owaidy and H.Y. Mohamed. "On the periodic solutions for nth order difference equations". Journal of Applied Mathematics and Computation , (to appear); "The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations". Journal of Applied Mathematics and Computation , (to appear)] to simplify the use of Carvalho's method to the case of discrete difference equations, in order to find the periodic solutions of second order linear difference equations. We can also find the complex periodic solutions. 相似文献
16.
Acta Mathematicae Applicatae Sinica, English Series - This paper mainly focus on the global existence of the strong solutions for the generalized Navier-Stokes equations with damping. We obtain the... 相似文献
17.
Existence and uniqueness theorems for parabolic stochastic partial differential equations with space—time white noise are
proved. The method is a combination of the characterization theorem for Hida distributions with the Feynman—Kac and Girsanov
formulae.
Accepted 3 December 1996 相似文献
18.
We present sufficient conditions for the linear asymptotic equilibrium of linear differential equations in Hilbert and Banach spaces. The results obtained are applied to studying the asymptotic equivalence of two linear differential equations. 相似文献
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研究非齐次Burgers方程Cauchy问题解的大时间行为.假定初值是周期的并且非齐次项具有多个零点.对初值的某些假定条件下,证明了问题的解收敛于一个行波解.所用的主要方法是广义特征线理论. 相似文献