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一类三维拟线性双曲型方程交替方向有限元法 总被引:2,自引:0,他引:2
对一类一般的三维拟线性双曲型方程通过转化二阶时间导数得到关于一阶时间导数的耦合方程组,然后进行离散得到交替方向有限元格式,应用微分方程先验估计的理论和技巧得到了最优阶H~1-模和L~2-模误差估计,并给出了数值算例,数值结果和理论分析得到很好的吻合. 相似文献
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汪瑶瑶 《纯粹数学与应用数学》2017,33(1)
研究双曲平均曲率流中一类几何流方程周期解的爆破问题.引入合适的黎曼不变量,将该方程化为对角型的一阶拟线性双曲型方程组.该方程组在Lax意义下不是真正非线性的.假设初值是周期的,且在一个周期内全变差很小,此外假设初值还满足一定的结构条件,可以证得该几何流方程的周期解必在有限时间内发生爆破,解的生命跨度估计可以给出. 相似文献
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二个自变量的二阶线性双曲型方程auxx+2buxy+cuyy+dux+euy+g=0,当系数a,b,c,d,e,g满足一定条件时,可以利用变换T:ξ=φ(x,y),η=ψ(x,y)化为一阶线性常微分方程求解,本文给出了求解定理和计算方法. 相似文献
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本文提出并研究带有线性外力场的双曲平均曲率流,通过凸曲线的支撑函数,导出一个双曲型Monge-Ampère 方程并将其转化成Riemann 不变量满足的拟线性双曲方程组。利用拟线性双曲方程组Cauchy 问题的局部解理论,讨论带有线性外力场的双曲平均曲率流Cauchy 问题经典解的生命跨度(即局部解存在的最大时间区间)。 相似文献
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本文讨论了2m阶双曲型方程具有奇性斜导数的边值问题,在边界奇点子流形的一定假设下,证明了所论问题在Sobolev空间H^s,s(Q)中解的存在性和唯一性,从而将二阶双曲方程的相应问题的已有的结果推广到了高维的情形。 相似文献
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陈明飞 《高等学校计算数学学报》1989,(3)
一、引 言 对于一阶线性偏微分方程和一阶线性双曲型方程组的有限元方法的误差分析,已有不少结果。本文讨论的是一类拟线性双曲型方程组的有限元方法的误差问题. 本文的结果对N个方程的方程组成立。为了方便起见,考虑如下的二个方程的方程组: 相似文献
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Drumi D. Bainov Zdzislaw Kamont Emil Minchev 《Journal of Computational and Applied Mathematics》1995,60(3):379-388
Strong and weak comparison principles for impulsive hyperbolic equations of first order are proved. Uniqueness criterion is obtained. 相似文献
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Guo Chun Wen 《数学学报(英文版)》2011,27(10):2051-2064
The present paper deals with oblique derivative problems for second order nonlinear equations of mixed type with degenerate
hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations
is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of
solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point principle.
In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions
in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order
equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients,
and then the advantage of complex analytic method can be applied. 相似文献
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Hideo Soga 《Mathematical Methods in the Applied Sciences》2019,42(11):3950-3966
In this paper, we propose a hyperbolic system of first‐order pseudo‐differential equations as generalization of the Maxwell equation. We state basic properties of this system corresponding to the ones of the (usual) Maxwell equation and explain that several known generalized Maxwell equations presented by some researchers can be integrated into the system. Namely, their equations can be regarded as our equation in special cases. Their generalized equations admit not only transversal but also longitudinal waves and are examined from the physical viewpoint. Using the present system, from the mathematical viewpoint, we interpret the meaning for presence of the longitudinal wave (with the transversal one) in their generalized equations. This presence means existence of more than one non‐zero characteristic root for the system (ie, non‐zero eigenvalue of the symbol). We prove also that our system becomes a first‐order expression of (generalized) elastic equations. Furthermore, it is shown that introducing the elastic equations implies expressing the generalized Maxwell equations by the potentials. 相似文献
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We consider the Cauchy problem for homogeneous linear third order weakly hyperbolic equations with time depending coefficients. We study the relation between the regularity of the coefficients and the Gevrey class in which the Cauchy problem is well-posed. 相似文献
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N. Parhi 《Czechoslovak Mathematical Journal》2000,50(1):155-173
In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of nth order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations. 相似文献
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关于一类二阶非线性双曲型方程全离散有限元方法的稳定性和收敛性估计 总被引:1,自引:0,他引:1
刘小华 《高等学校计算数学学报》2002,24(1):15-22
1 引 言考虑如下混合问题 :φ( x,u) utt- di,j=1 xi( aij( x,u) u xj) - di=1bi( x,u) uxi =f( x,u) ( x,t)∈Ω× [0 ,T]u( x,0 ) =0 , ut( x,0 ) =0 x∈Ωu( x,t) =0 ( x,t)∈ Ω× [0 ,T]( 1 .1 )这里 utt= 2 u t2 ,uxi= u xi;Ω是 Rd 中充分光滑的有界开域 ,边界 Ω光滑 .对于 φ( x,u)中仅含有 x,或 φ( x,u)≡ 1的线性或非线性双曲型方程的半离散或全离散有限元方法的研究已有 [1 ] -[4 ] .这些文献定义了线性[1 ] [4] 或非线性[2 ] 或预测—校正[4] 全离散有限元格式 ,然后将原方… 相似文献
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D. P. Babii S. K. Godunov V. T. Zhukov O. B. Feodoritova 《Computational Mathematics and Mathematical Physics》2007,47(3):427-441
Issues concerning difference approximations of overdetermined systems of hyperbolic equations are examined. The formulations of extended overdetermined systems are given for hydrodynamics equations, magnetohydrodynamics equations, Maxwell equations, and elasticity equations. Some approaches to the construction of difference schemes are discussed for these systems. 相似文献
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We study the initial behaviour of the characteristics of an hyperbolic system of first‐order equations, which models the diffusion of n species of stable isotopes of the same element in a medium. The model is based on the assumption that, since the isotopes are chemically indistinguishable, the flux of each isotope depends on the gradient of the total concentration of the element weighted by the relative percentage of the isotope. We consider here the influence of initial irregularities of the total concentration on the characteristics. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Monotone iterative methods for impulsive hyperbolic differential-functional equations 总被引:4,自引:0,他引:4
Drumi D. Bainov Zdzislaw Kamont Emil Minchev 《Journal of Computational and Applied Mathematics》1996,70(2):329-347
Theorems on impulsive hyperbolic differential-functional inequalities are considered. Comparison results and a uniqueness criterion are obtained. A method of approximation of the solutions of impulsive hyperbolic differential-functional equations by means of solutions of the associated linear problems is established. The difference between the exact and the approximate solutions is estimated. 相似文献