共查询到20条相似文献,搜索用时 31 毫秒
1.
D. S. Anikonov S. G. Kazantsev D. S. Konovalova 《Journal of Applied and Industrial Mathematics》2013,7(3):313-325
We study some questions of the qualitative theory of differential equations. A Cauchy problem is considered for a hyperbolic system of two first-order differential equations whose right-hand sides contain some discontinuous functions. A generalized solution is defined as a continuous solution to the corresponding system of integral equations. We prove the existence and uniqueness of a generalized solution and study the differential properties of the obtained solution. In particular, its first-order partial derivatives are unbounded near certain parts of the characteristic lines. We observe that this property contradicts the common approach which uses the reduction of a system of two first-order equations to a single second-order equation. 相似文献
2.
研究二维空间中一类耦合非线性Klein-Gordon方程组的整体解.首先,通过构造交叉强制变分问题且建立发展流的交叉不变流形,得到了该方程组解爆破和整体存在的一个最佳条件.然后利用尺度变换讨论证明了当初值为多小时,该方程组的整体解存在. 相似文献
3.
E. V. Vvedenskaya 《Differential Equations》2009,45(2):262-266
We consider the optimal recovery problem for a solution of a system of linear homogeneous ordinary differential equations with constant self-adjoint coefficient matrix on the basis of inexactly given values of the solution at two time instants. 相似文献
4.
A. M. Denisov 《Computational Mathematics and Mathematical Physics》2014,54(10):1513-1521
An initial boundary-value problem for a quasilinear system of partial differential equations with a nonlocal boundary condition involving a delayed argument is considered. The existence of a unique solution to this problem is proved by reducing it to a system of nonlinear integral-functional equations. The inverse problem of finding a solution-dependent coefficient of the system from additional information on a solution component specified at a fixed point of space as a function of time is formulated. The uniqueness of the solution of the inverse problem is proved. The proof is based on the derivation and analysis of an integral-functional equation for the difference between two solutions of the inverse problem. 相似文献
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具有热储备的可修复平行系统在由常规错误引起失效下的渐进稳定性 总被引:3,自引:1,他引:2
胡薇薇 《应用泛函分析学报》2006,8(1):5-20
讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用Banach空间的Volttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由于初始值不在定义域内,故得到的是mild解.但在t>0时系统古典解存在唯一,所以此时mild解即为古典解.最后,利用线性算子半群稳定性的结果,证明了该动态解在范数意义下收敛到稳态解,进而得到了系统的渐进稳定性. 相似文献
8.
《Journal of the Egyptian Mathematical Society》2014,22(1):90-95
Recently, [1] have obtained the transient solution of multi-server queue with balking and reneging. In this paper, a similar technique is used to drive a new elegant explicit solution for a two heterogeneous servers queue with impatient behavior. In addition, steady-state probabilities of the system size are studied and some important performance measures are discussed for the considered system. 相似文献
9.
Given a nonlinear control system for which an admissible statetrajectory is specified, we solve approximately the input outputdecoupling problem around this nominal trajectory. An approximatesolution for this problem is obtained by dealing with the linearizedsystem along this trajectory. An exact solution to the inputoutput decoupling problem for the linearization is shown tobe an approximate solution to the input output decoupling problemaround the nominal trajectory for the original nonlinear system.In a similar way, we provide an approximate solution to thedisturbance decoupling problem around a specified trajectoryof the nonlinear system. The nonlinear model of a two link robotmanipulator is used to illustrate the results on input outputdecoupling. 相似文献
10.
Yu. N. Shishmareva 《Differential Equations》2008,44(3):428-433
For the simplest hyperbolic system of string vibration equations in a special admissible domain whose boundary contains a characteristic segment of the system, we consider two problems of Riemann-Hilbert type and find existence and uniqueness conditions for the generalized solution of these problems in weighted classes of continuous functions. 相似文献
11.
For a singularly perturbed system of two second-order differential equations (one rapid and one slow), we prove the existence
of a solution and obtain its asymptotics for the case in which the degenerate equation has two intersecting roots. In addition,
we show that this solution is an asymptotically stable stationary solution of the corresponding parabolic problem and find
its local attraction domain. 相似文献
12.
Seymour Singer 《Annali di Matematica Pura ed Applicata》1971,89(1):1-29
Summary The author demonstrates the existence of a smooth solution to a singular initial value problem for a quasiliuear hyperbolic
equation in two independent variables. The problem is transformed into an equivalent system of integral equations for which
a solution is obtained by invoking Schauder’s fixed point theorem.
Entrata in Redazione il 19 ottobre 1970. 相似文献
13.
In this paper, we introduce a new iterative sequence which is constructed by using the new modified two block hybrid projection method for solving the common solution problem for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain conditions, and the common fixed point problems for families of uniformly quasi - ${\phi}$ - asymptotically nonexpansive and locally uniformly Lipschitz continuous. Strong convergence theorems are proved on approximating a common solution of a system of generalized equilibrium problems and fixed point problems for two countable families in Banach spaces. Our results presented in this paper improve and extend many recent results in this area. 相似文献
14.
The aim of this paper is to outline the numerical solution ofa reactiondiffusion system describing the evolution ofan epidemic in an isolated habitat. The model we consider isdescribed by two weakly coupled semi-linear parabolic equationsand we introduce a finite difference scheme for its numericalsolution. We study the behaviour of the exact solution by meansof the numerical scheme. We show the positivity, the decreaseand the decay to extinction of the numerical solution. Finallywe report the results of the numerical tests; in these simulationswe observe that the asymptotic behaviour of the reaction-diffusionsystem is the same as that of the associated ODE system (KermackMcKendrickmodel). 相似文献
15.
We consider a basic duplex system characterized by warm standby and attended by two general heterogeneous repairmen. In order to derive computational results for the point availability of the engineering system, we first employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations. However, an explicit evaluation of the (exact) solution is in general excluded. Therefore, we also propose a numerical solution of the equations. Our methodology is based on new modification of the first-order upwind scheme applied to a semiinfinite region. As an application, we consider the important case of Weibull–Gnedenko repair and provide an in-depth analysis of some key features of the duplex system. 相似文献
16.
A Global Solution to a
Two-dimensional Riemann Problem Involving Shocks as Free
Boundaries 总被引:4,自引:0,他引:4
YuxiZheng 《应用数学学报(英文版)》2003,19(4):559-572
We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values. 相似文献
17.
翁佩萱 《应用数学学报(英文版)》1996,12(1):11-21
WENGPEIXUAN(翁佩萱)(DepartmentofMathematics,SouthChinaNormalUniversity,Guangzhou510631,China)GLOBALATTRACTIVITYINAPERIODICCOMPET... 相似文献
18.
具有常规原因和人为错误的两个不同部件平行系统解的性质 总被引:1,自引:0,他引:1
讨论了一个由于常规原因和人为错误引起故障的两不同部件并行系统的模型,修复后的故障系统恢复正常.在假设修复率非常数的前提下,运用纯分析的方法给出了两不同部件并行系统解的性质,绕过了该系统解是否存在的问题. 相似文献
19.
Numerical analysis for a conservative difference scheme to solve the Schrödinger-Boussinesq equation
Luming Zhang Dongmei BaiShanshan Wang 《Journal of Computational and Applied Mathematics》2011,235(17):4899-4915
In this paper, we present a finite difference scheme for the solution of an initial-boundary value problem of the Schrödinger-Boussinesq equation. The scheme is fully implicit and conserves two invariable quantities of the system. We investigate the existence of the solution for the scheme, give computational process for the numerical solution and prove convergence of iteration method by which a nonlinear algebra system for unknown Vn+1 is solved. On the basis of a priori estimates for a numerical solution, the uniqueness, convergence and stability for the difference solution is discussed. Numerical experiments verify the accuracy of our method. 相似文献
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根据给定输入和初始状态求解系统的状态方程是系统分析的关键步骤。针对系统输入具有指数形式或可等价于指数形式进行研究,给出了这种情况下的一种求特解的有效方法,并特别就二阶系统给出了一种快速有效求解方法。最后通过两个典型系统的求解验证了该方法的简便性和有效性。 相似文献