共查询到20条相似文献,搜索用时 109 毫秒
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李林锐 《数学的实践与认识》2018,(3)
研究了一类新的修正的Leray-α磁流体动力学方程组的初始值问题,利用方程的耦合结构,通过采用能量方法、紧性方法、Sobolev嵌入法等,证明了模型解在二维情形下解的整体存在性. 相似文献
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本文给出了理想磁流体动力学方程组的经典解在初始扰动适当大的情况下破裂的结果.文[1]证明了描述多方理想可压缩气体运动的欧拉系统的经典解在初始扰动适当大的情况下破裂的结果.本文将利用和文[1]相似的方法证明所得定理. 相似文献
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雷震 《数学年刊A辑(中文版)》2005,(2)
本文给出了理想磁流体动力学方程组的经典解在初始扰动适当大的情况下破裂的结果.文[1]证明了描述多方理想可压缩气体运动的欧拉系统的经典解在初始扰动适当大的情况下破裂的结果.本文将利用和文[1]相似的方法证明所得定理. 相似文献
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本文讨论了能量方程是压力一密度关系的一维半导体流体动力学模型方程,通过把欧拉-泊松方程变成拟线性波动方程,利用拟线性波动方程的局部解存在性,得到一维半导体流体动力学模型的局部解,并且解是有界的。 相似文献
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我们考虑周期边条件下二维磁流体动力学(MHD)方程,证明了指数吸引子的存在性并给出其分形维度的上界估计. 相似文献
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N. M. Borodachev 《Journal of Applied Mathematics and Mechanics》2001,65(6):1021-1024
Nine equations of compatibility of deformations are obtained in which, unlike the classical Saint-Venant compatibility equations, only first derivatives with respect to the coordinates occur. It is proved that, of these nine equations, only six are independent. It is shown that the classical compatibility equations can be obtained from these equations. 相似文献
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Shreeram S. Abhyankar Nicholas F. J. Inglis 《Transactions of the American Mathematical Society》2001,353(7):2941-2969
Previously nice vectorial equations were constructed having various finite classical groups as Galois groups. Here such equations are constructed for the remaining classical groups. The previous equations were genus zero equations. The present equations are strong genus zero.
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In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with “small” initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with “small” initial data. 相似文献
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P. K. Galenko V. G. Lebedev A. A. Sysoeva 《Computational Mathematics and Mathematical Physics》2011,51(6):1074-1090
The critical dynamics of a spatially inhomogeneous system are analyzed with allowance for local nonequilibrium, which leads
to a singular perturbation in the equations due to the appearance of a second time derivative. An extension is derived for
the Eyre theorem, which holds for classical critical dynamics described by first-order equations in time and based on the
local equilibrium hypothesis. It is shown that gradient-stable numerical algorithms can also be constructed for second-order
equations in time by applying the decomposition of the free energy into expansive and contractive parts, which was suggested
by Eyre for classical equations. These gradient-stable algorithms yield a monotonically nondecreasing free energy in simulations
with an arbitrary time step. It is shown that the gradient stability conditions for the modified and classical equations of
critical dynamics coincide in the case of a certain time approximation of the inertial dynamics relations introduced for describing
local nonequilibrium. Model problems illustrating the extended Eyre theorem for critical dynamics problems are considered. 相似文献
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Pingrun Li 《Journal of Applied Analysis & Computation》2019,9(3):1071-1082
In this paper, we study a class of singular integral-different equations of convolution type with Cauchy kernel. By means of the classical boundary value theory, of the theory of Fourier analysis, and of the principle of analytic continuation, we transform the equations into the Riemann-Hilbert problems with discontinuous coefficients and obtain the general solutions and conditions of solvability in class $\{0\}$. Thus, the result in this paper generalizes the classical theory of integral equations and boundary value problems. 相似文献
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Yipeng Shi 《偏微分方程(英文版)》2001,14(3):193-206
In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this, we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas. 相似文献
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Jiang Xu 《Journal of Differential Equations》2012,252(2):915-940
Two relaxation limits in critical spaces for the scaled nonisentropic Euler–Poisson equations with the momentum relaxation time and energy relaxation time are considered. As the first step of this justification, the uniform (global) classical solutions to the Cauchy problem in Chemin–Lerner?s spaces with critical regularity are constructed. Furthermore, by the compactness argument, it is rigorously justified that the scaled classical solutions converge to the solutions of energy-transport equations and drift-diffusion equations, respectively, with respect to different time scales. 相似文献
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The equations of linear elasticity for rotationally symmetric deformations are expanded using a small parameter related to the thickness to radius of curvature ratio of the shell to obtain the classical thin shell equations of conical shells as a first approximation. These classical equations with variable coefficients permit further asymptotic expansions in the cases of steep as well as shallow cones, yielding systems of equations with constant coefficients. Solutions of these equations are used to compute the influence coefficients relating edge loads and edge displacements. 相似文献
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A. G. Kushner 《Russian Mathematics (Iz VUZ)》2008,52(4):38-52
The present paper is devoted to the problem of transforming the classical Monge-Ampère equations to the linear equations by change of variables. The class of Monge-Ampère equations is distinguished from the variety of second-order partial differential equations by the property that this class is closed under contact transformations. This fact was known already to Sophus Lie who studied the Monge-Ampère equations using methods of contact geometry. Therefore it is natural to consider the classification problems for the Monge-Ampère equations with respect to the pseudogroup of contact transformations. In the present paper we give the complete solution to the problem of linearization of regular elliptic and hyperbolic Monge-Ampère equations with respect to contact transformations. In order to solve this problem, we construct invariants of the Monge-Ampère equations and the Laplace differential forms, which involve the classical Laplace invariants as coefficients. 相似文献