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1.
向建林  欧卓玲 《应用数学》2013,26(1):146-154
可压缩欧拉-泊松方程组描述的是具自引力势能气态星体内部气体的运动变化.对于满足质量守恒和能量守恒的一些速度场,本文在熵函数的光滑性较弱的条件下研究欧拉-泊松方程组平衡解的存在性.在本文中,作者应用变分方法得到6/5<γ<2时方程组平衡解的存在性结果.该结果减弱了关于非旋转星体欧拉-泊松方程组平衡解存在的条件,从而适用于更一般的物理环境.  相似文献   

2.
本文证明了具零特征且形式更广泛的一类拟线性双曲型方程组的具有一般非线性边界条件的混合初 一边值问题半整体C1解的存在唯一性.  相似文献   

3.
一类拟线性双曲型方程组混合初-边值问题的半整体C1解   总被引:1,自引:0,他引:1  
于立新 《数学年刊A辑》2004,25(5):549-560
本文证明了具零特征且形式更广泛的一类拟线性双曲型方程组的具有一般非线性边界条件的混合初-边值问题半整体C1解的存在唯一性.  相似文献   

4.
研究一类具非线性扩散系数的中立双曲型阻尼偏微分方程组的振动性.通过利用R iccati变换、微积分技巧,获得了该方程组在两类边值条件下解振动的一些充分条件.  相似文献   

5.
拟线性对称双曲组具有特征边界的初边值问题   总被引:4,自引:0,他引:4  
拟线性对称双曲组在数学物理中有广泛的应用.例如,流体力学方程组就可化为拟线性对称双曲组进行讨论.在文[1,2]中,对于拟线性对称双曲组具非特征边界的初边值问题已作了完整的讨论,但对于边界为特征的情形,附加了方程组中未知函数导数项的系数不依赖于u的要求.在等熵、初速为亚音速,初始密度接近于常数的固壁边界问题,  相似文献   

6.
考虑一个具阻尼和源项的非线性粘弹热方程组的初边值问题.建立一个正初始能量下方程组解的爆破结果.  相似文献   

7.
本文根据高维非线性守恒律方程组的研究历程将这一领域的研究大体分为四个阶段: 局部经典解、具扇状波结构弱解、具花状波结构弱解、整体解与混合型方程. 本文据此线索回顾与介绍多年来在该领域所获得的主要成果与进展, 并提出今后所面临的一些未解决的重要问题及困难.  相似文献   

8.
本文研究具弱衰减、小初值初始条件的一维Dirac-Klein-Gordon方程组解的存在时间估计问题,结果表明这类问题解的存在时间几乎比e-4大初值的弱衰减条件使得通常的方法不能使用,在此,通过利用Delort曾用过的方程组特征的曲率性质以及2次微局部椭圆正则性解决了该问题.  相似文献   

9.
林支桂 《中国科学A辑》2003,33(6):587-596
考虑半空间上具耦合非线性边界条件的热方程组解的爆破估计. 给出了爆破速率的上界和下界估计, 得到了具零初值解的惟一性和非惟一性结果.  相似文献   

10.
文章应用差分特征列方法研究一类具有生物性质的非线性差分方程组.首先介绍差分特征列及Z变换的重要定义、定理.接下来通过将生物模型方程组Ⅰ.Ⅱ按照有效化、求特征列、判断一致性及不可约性等步骤获得方程组Ⅰ.Ⅱ的特征列集和零点集,最后结合Z变换法分别得到方程组Ⅰ.Ⅱ的零点集的一组精确解.  相似文献   

11.
In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.  相似文献   

12.
In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.  相似文献   

13.
Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.  相似文献   

14.
Abstract

This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dynamics are stable while impulses are unstable; (2) impulses are stable while continuous dynamics are unstable. To begin with, based on Lyapunov method as well as graph-theoretic technique, several new stability criteria in two cases are derived, that are, the Lyapunov-type criteria and the coefficients-type criteria. Then main results are used for a class of random impulsive coupled oscillators. Finally, the effectiveness of the obtained results is verified by numerical simulations.  相似文献   

15.
The global asymptotic behavior of dynamical systems on compact metric spaces can be described via Morse decompositions. Their components, the so-called Morse sets, are obtained as intersections of attractors and repellers of the system. In this paper, new notions of attractor and repeller for nonautonomous dynamical systems are introduced which are designed to establish nonautonomous generalizations of the Morse decomposition. The dynamical properties of these decompositions are discussed, and nonautonomous Lyapunov functions which are constant on the Morse sets are constructed explicitly. Moreover, Morse decompositions of one-dimensional and linear systems are studied.

  相似文献   


16.
Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.  相似文献   

17.
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.  相似文献   

18.
The properties of matrix-valued polynomials generated by the scalar-type Rodrigues’ formulas are analyzed. A general representation of these polynomials is found in terms of products of simple differential operators. The recurrence relations, leading coefficients, completeness are established, as well as, in the commutative case, the second order equations for which these polynomials are eigenfunctions and the corresponding eigenvalues, and ladder operators.A new, direct proof is given to the conjecture of Durán and Grünbaum that if the weights are self-adjoint and positive semidefinite then they are necessarily of scalar type.Commutative classes of orthogonal polynomials (corresponding to weights that are self-adjoint but not positive semidefinite) are found, which satisfy all the properties usually associated to orthogonal polynomials, and are not of scalar type.  相似文献   

19.
In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10471048)  相似文献   

20.
In this work, a class of nonstandard finite difference (NSFD) schemes are proposed to approximate the solutions of a class of generalized convection–diffusion–reaction equations. First, in the case of no diffusion, two exact finite difference schemes are presented using the method of characteristics. Based on these two exact schemes, a class of exact schemes are presented by introducing a parameter α. Second, since the forms of these exact schemes are so complicated that they are not convenient to use, a class of NSFD schemes are derived from the exact schemes using numerical approximations. It follows that, under certain conditions about denominator function of time‐step sizes, these NSFD schemes are elementary stable and the solutions are positive and bounded. Third, by means of the Mickens' technique of subequations, a new class of implicit NSFD schemes are constructed for the full convection–diffusion–reaction equations. It is shown that, under certain parameters set, these NSFD schemes are capable of preserving the non‐negativity and boundedness of the analytical solutions. Finally, some numerical simulations are provided to verify the validity of our analytical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1288–1309, 2015  相似文献   

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