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<正> 在文[1]中我们研究了一类特殊非线性双曲型方程组(?)的 Cauchy 问题.同时在文[1]的引言中我们曾经指出,对于一般的一阶非线性双曲型方程组 相似文献
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鄢盛勇 《数学的实践与认识》2011,41(15)
用函数论的方法研究了三类超定双曲型方程组的解,即三类多双曲复方程组在一般柱形域上的Riemann-Hilbert边值问题的提法,可解条件,解的表示,唯一性和存在性. 相似文献
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§1引言 如所周知,Lax-Friedrichs格式是P.D.Lax对拟线性双曲型守恒律方程组提出的一种有限差分格式。若得到了其相应的差分逼近解的收敛性,这格式不仅提供了证明:整体广义解存在性的一种理想途径,而且能方便有效地直接用来进行整体解的数值计算。在单个守恒律方程情形,O.Oleinik,C.Conway and J.Smoller等证明了这一格式的收敛性,并得到了整体广义解的存在性。然而,对双曲型方程组,特别是气体动力学方程组,Lax-Friedrichs格式的收敛性一直没有什么结果。 相似文献
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1.本文研究对称双曲型方程组式中为自变量,A_i,B为m×m方阵,A_i是对称的。在数学物理中时常遇见这种类型的方程,K.O.Friedrichs最先系统地研究了这个方程,解决了它的Cauchy问题。G.D.F.Duff在考虑一般双曲型方程的边值问题时,也曾用解析逼近法,解出它的混合问题。 K.O.Friedrichs后来又系统地发展了正对称型方程组理论,它以对称双曲型方程 相似文献
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广义Sine-Gordon型非线性高阶双曲方程组 总被引:14,自引:0,他引:14
<正> 本文讨论高阶非线性双曲型方程组的周期边界问题与初值问题整体广义解与整体古典解的存在性、唯一性及它们的光滑性. 有很多作者对所谓Sine-Gordon方程 相似文献
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许勇强 《数学年刊A辑(中文版)》2012,33(5):557-578
首先研究了带有非线性记忆的双曲方程组解的局部存在性.然后,在N=1的情况下,证明了小初值解的全局存在性,并给出了当t→∞时的渐近性态.最后在N≥1且初值是正的情况下,导出了全局解的非存在性结果. 相似文献
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一类脉冲时滞双曲型方程组解的振动性 总被引:5,自引:0,他引:5
本文研究含脉冲的时滞双曲型方程组解的振动性,利用二阶脉冲微分不等式的性质,得到了方程组在两类不同边界条件下解振动的一些充分判据. 相似文献
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非线性高阶抛物双曲型耦合方程组的第一边界问题 总被引:1,自引:0,他引:1
陈国旺 《数学年刊A辑(中文版)》1988,(2)
本文研究了一类广义Sine-Gordon型非线性高阶双曲方程组、非线性高阶拟双曲型方程组、非线性高阶拟抛物型方程组以及非线性高阶广义Sehrdinger型方程组的耦合方程组的第一边界问题,作者证明了此耦合方程组第一边界问题的整体广义解和整体古典解的存在性、唯一性和光滑性。 相似文献
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Ravi P. Agarwal 《Journal of Computational and Applied Mathematics》1979,5(2):117-123
The paper deals with the second order differential systems with periodic boundary conditions. In the first part of the paper four different methods are employed to find the unique solution of the linear systems. One of the methods is a shooting type which converts the periodic boundary value problem into its equivalent initial value problem. In the second part of the paper several sufficient conditions are provided for the existence and uniqueness for the nonlinear systems. The technique developed for the linear systems to convert into its equivalent initial value problem is used in an iterative way for the nonlinear systems. It is shown that the iterations converge quadratically. 相似文献
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本文讨论了一阶非连续微分系统初值问题和边值问题,在方程右端函数不连续并且不具有任何单调性的情况下,给出了方程的唯一解,并且给出了收敛于方程解的迭代序列。 相似文献
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We consider the Cauchy problem for a class of systems of ordinary differential equations of large dimension.We prove that, for sufficiently large number of equations, the last component of a solution to the Cauchy problem is an approximate solution to the initial value problem for a delay differential equation. Estimates of the approximation are obtained. 相似文献
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Systems governed by ordinary differential equations with continuous,switching and impulse controls 总被引:1,自引:0,他引:1
Jiongmin Yong 《Applied Mathematics and Optimization》1989,20(1):223-235
Optimal control problem for systems governed by ordinary differential equations with continuous, switching and impulse controls are studied. It is proved that the value function of the problem is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman system. 相似文献
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A special boundary value problem is studied for the Lyapunov differential equation which is used for investigation of the asymptotic properties of solutions to systems of periodic differential equations with a parameter. An algorithm is proposed for constructing an approximate solution to this boundary value problem, and conditions on the parameter are found under which the zero solution to the system is asymptotically stable. 相似文献
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A. S. Il’inskii T. N. Galishnikova 《Moscow University Computational Mathematics and Cybernetics》2008,32(4):187-193
A 3D problem of reflection of a plane electromagnetic wave by a local impedance section of a wavy surface is considered. The boundary value problem for the system of Maxwell’s equations in a region with an irregular boundary is reduced to solution of systems of hypersingular integral equations. A numerical algorithm is proposed for solution of these systems. Results of numerical computations are presented. 相似文献
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Li Mingzhong 《数学年刊B辑(英文版)》1990,11(1):84-92
In this paper,based on previous results,the Riemann-Hilbert boundary valueproblems with general forms for overdetermined elliptic equations of first order are consi-dered.The characteristic of modified function space is given.It is proved that there existsa unique solution for modified problem of the problem which we discuss.By the way,itis pointed out that there are great differences between overdetermined elliptic systems andfirst order elliptei systems in the plane. 相似文献
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A. A. Abramov V. I. Ul’yanova L. F. Yukhno 《Computational Mathematics and Mathematical Physics》2009,49(3):474-481
The index of the homogeneous self-adjoint boundary value problem for the Hamiltonian systems of ordinary differential equations is introduced. It is assumed that the system has a nontrivial solution. The relationship between the index of an eigenvalue of the nonlinear eigenvalue problem and the index of the corresponding homogeneous problem is established. Properties of the index of the problem and those of the eigenvalue are examined. 相似文献
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D. A. Fetisov 《Differential Equations》2016,52(12):1638-1649
We consider the construction of solutions of terminal problems for multidimensional affine systems. We show that the terminal problem for a regular system in quasicanonical form can be reduced to a boundary value problem for a system of ordinary differential equations of lower order with right-hand side depending on a vector parameter. We prove a sufficient condition for the existence of a solution of the above-mentioned boundary value problem. A method for constructing a numerical solution is developed. 相似文献