共查询到19条相似文献,搜索用时 109 毫秒
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考虑了关于二维守恒律的大时间步长Godunov方法.该方法是关于一维问题的自然推广.证明了文中给出的数值流函数下,该方法是守恒的.进一步还给出了近似Riemann解应满足的条件,并且证明了利用满足这些条件的近似Riemann解的大时间步长Godunov方法守恒.最后,补充证明了满足这些条件的近似Riemann解是满足熵条件的. 相似文献
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双曲型守恒律组的一类差分格式及其熵条件 总被引:1,自引:0,他引:1
其中u(x,t)=(u_1(x,t),…,u_m(x,t))~T,f(u(x,t))=(f_1(u(x,t)),…,f_m(u(x,t)))~T,f的Jacobian记为 A(u)=?f(u)/?u,具有m个实特征值λ_1(u)≤λ_2(u)≤… ≤λ_m(u)以及完备的古特征向量系{γ_k(u)}_k~m=1.对区域R~+={(x,t)|x∈(-∞,+∞),t∈ 相似文献
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刘海亮 《高校应用数学学报(A辑)》1996,(3):277-282
本文研究了非凸双曲守恒律ut+(u^3)x=0解的渐近性态。对于初值具有紧支集或周期函数的情形,我们利用广义特征原理,建立了关于波速总变差的基本递推估计,给出了解的最优衰减速率。 相似文献
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本文研究一类二维单个守恒律方程的Riemann问题.用广义特征分析方法研究了这类方程,给出了基本波的分类,解决了初值为两片常数的二维Riemann问题,给出了Riemann解. 相似文献
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杨小舟 《数学物理学报(A辑)》2005,25(4):584-592
该文提出了一种非线性变换把一类n维单守恒律方程和初值同时降维为一维, 得到非自相似形式的全局解和基本波的表达式,并发现了非自相似解和相似解之间的本质性差别和联系 相似文献
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我们研究了具有周期初值数据的标量守恒律的方程的解的大时间行为,在很弱的非线性条件下,我们证明了当时间趋于无穷时其解收敛于一常数,本文的结果改进了以前的结果,因为我们只需在初值数据的平均值处流量是非线性的。 相似文献
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Jiaxin Hu 《数学学报(英文版)》1999,15(3):317-332
A two-dimensional hyperbolic system of nonlinear conservation laws is considered for any piecewise constant initial data having
two discontinuity rays with the origin as vertex. One kind of new waves, which is labeled the Dirac-contact wave, appears
in the solution. The entropy conditions for the Dirac-contact waves are given. The solutions on the Dirac-contact waves can
be viewed as the bounded linear functionals onC
0
∞
(R
2 ×R
+).
Supported by CNSF and a grant from Academia Sinica
Author’s current address: CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France 相似文献
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Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation 下载免费PDF全文
Ben Yang Yunjia Song Yanzhi M Xinxue Zhang 《Journal of Nonlinear Modeling and Analysis》2023,5(4):708-719
Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers. 相似文献
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We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and corresponding characteristic fields to be linearly degenerate. The approach is based on our careful construction of more accurate auxiliary approximation to weakly nonlinear geometric optics, the properties of wave front-tracking approximate solutions, the behavior of solutions to the approximate asymptotic equations, and the standard semigroup estimates. To illustrate this approach more clearly, we focus first on the Cauchy problem for the hyperbolic systems with compact support initial data of small bounded variation and establish that the L 1-estimate between the entropy solution and the geometric optics expansion function is bounded by O(?2), independent of the time variable. This implies that the simpler geometric optics expansion functions can be employed to study the behavior of general entropy solutions to hyperbolic systems of conservation laws. Finally, we extend the results to the case with non-compact support initial data of bounded variation. 相似文献
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In this paper, we investigate Lie symmetry group, optimal system, exact solutions and conservation laws of modified hyperbolic geometric flow via Lie symmetry method. Then, conservation laws of modified hyperbolic geometric flow are obtained by applying Ibragimov method. 相似文献
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Hu Xingbiao 《偏微分方程(英文版)》1990,3(4)
In this paper, first a class of Hirota-type equations Σ^l_{k=1}H_k(D_x,D_t,D_y)[F_k(D_x,D_t,D_y)f • f] • [G_k(D_x,D_t,D_y)f • f] = 0 are considered. By imposing certain conditions on F_k,G_k and H_k, we show that the abovementioned equation possesses one-soliton solution. Secondly we present a new integrable equation which is an extention of Novikov-Veselov equation and Ito equation. We obtain a Băcklund transformation (BT) of this equation. Finally we consider a generalized equation of Ramani and Sawada-Kotera, and obtain its BT. Starting with the BT an infinite number of conservation laws are derived. 相似文献
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We study in this paper the perturbation of elementary waves with interactions: overtaking of shock waves belonging to the same characteristic family and penetrating of a shock wave and a rarefaction wave belonging to the different characteristic family for 2 × 2 genuinely nonlinear strictly hyperbolic conservation laws. The entropy solutions for the perturbed problems are obtained by the Glimm's scheme. 相似文献
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In many applications, there arise systems of two nonlinear conservation laws with a single linearly degenerate characteristic field, or contact field, the speed of which may coincide with that of the genuinely nonlinear characteristic field along a curve. Along this coincidence curve, the contact field may have isolated singular points. We prove that under generic assumptions the singular points can be centers or saddles for the contact field. We construct the local Riemann solution for each of the two generic cases. This work sheds light on the classification of local Riemann solutions of systems of two conservation laws with a linearly degenerate characteristic field. 相似文献
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Yi ZHOU 《数学年刊B辑(英文版)》2022,43(4):499-508
Let u(t, x) be the solution to the Cauchy problem of a scalar conservation law in one space dimension. It is well known that even for smooth initial data the solution can become discontinuous in finite time and global entropy weak solution can best lie in the space of bounded total variations. It is impossible that the solutions belong to, for example, H1 because by Sobolev embedding theorem H1 functions are H¨older continuous. However, the author notes that from any point (t, x), he can draw a generalized characteristic downward which meets the initial axis at y = α(t, x). If he regards u as a function of (t, y), it indeed belongs to H1 as a function of y if the initial data belongs to H1 . He may call this generalized persistence (of high regularity) of the entropy weak solutions.The main purpose of this paper is to prove some kinds of generalized persistence (of high regularity) for the scalar and 2 × 2 Temple system of hyperbolic conservation laws in one space dimension. 相似文献