共查询到11条相似文献,搜索用时 15 毫秒
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1. Generalized Nonlinear Schrsdinger EquationThe Schr6dinger equation has been extensively used in physics research, particularlyin the modeling of nonlinear dispersion waves [8]. Numerical methods for solving theSchr6dinger equation have been discussed in the literature. In this article, we considera generalized nonlinear Schr6dinger equation with variable coefficientsi: ~ g(A(x)Z) iF(t)u B(x) lulp~' u = 0, iZ ~ ~l, P > 1, (1)where u(x, 0) ~ of (x). The coefficients A(x), F(t) and, … 相似文献
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This paper is devoted to discussing the discrete-ordinates method for the monoenergetic neutron transport equation in a slab with generalized boundary conditions. For homogeneous medium with isotropic scattering and fission, the convergence theorems for discrete-ordinates approximations are given respectively for critical eigenvalue problem and dominant eigenvalue problems: for inhomogeneous medium with anisotropic scattering and fission, a similar discussion and an estimation for the convergence rate are given for critical eigenvalue problems. Finally, some numerical results are given by use of this method. 相似文献
3.
CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME AND STABILITY FOR CONSERVATION LAWS WITH A DISCONTINUOUS SPACE-TIME DEPENDENT FLUX 总被引:4,自引:0,他引:4 下载免费PDF全文
The authors give the first convergence proof for the Lax-Friedrichs finite differencescheme for non-convex genuinely nonlinear scalar conservation laws of the formu_t f(k(x, t), u)_x = 0,where the coefficient k(x, t) is allowed to be discontinuous along curves in the (x, t)plane. In contrast to most of the existing literature on problems with discontinuouscoefficients, here the convergence proof is not based on the singular mapping approach,but rather on the div-curl lemma (but not the Young measure) and a Lax type en-tropy estimate that is robust with respect to the regularity of k(x, t). Following [14],the authors propose a definition of entropy solution that extends the classical Kruzkovdefinition to the situation where k(x, t) is piecewise Lipschitz continuous in the (x, t)plane, and prove the stability (uniqueness) of such entropy solutions, provided that theflux function satisfies a so-called crossng condition, and that strong traces of the solu-tion exist along the curves where k(x, t) is disco 相似文献
4.
莫嘉琪 《Annals of Differential Equations》2004,20(4):396-401
A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series, the boundary layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. 相似文献
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6.
Wang Youbin 《Annals of Differential Equations》2005,21(3):435-438
In this paper, we obtain some necessary and sufficient conditions for the oscillation of all positive solutions of a delay Logistic equation with continuous and piecewise constant arguments about the positive equilibrium. 相似文献
7.
SunFuqin WangMingxin 《偏微分方程(英文版)》2004,17(1):71-79
In this paper, we study the non-negative solutions to a degenerate parabolic system with nonlinear boundary conditions in the multi-dimensional case.By the upper and lower solutions method, we give the conditions on the existence and non-existence of global solutions. 相似文献
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A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the brine, radionuclid and heat are treated by a combination of a Galerkin finite element method and the method of characteristics. Optimal-order convergence in L2 is proved. Time-truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the brine, radionuclide and heal equalios, temporal and spatial error are lossened by direct compulation of the velocity in the mixed method, as opposed to differentiation of the pressure. 相似文献
9.
Yu Zanping Zhou Zheyan School of Math.and Computer Science Fujian Normal University Fuzhou ) Shen Jianhe 《Annals of Differential Equations》2007,23(3):365-372
The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above. 相似文献
10.
Feng Yuqiang Liu Sanyang 《Annals of Differential Equations》2005,21(3):271-274
The existence, multiplicity and uniqueness of positive solutions of a third order two point boundary value problem are discussed with the help of two fixed point theorems in cones, respectively. 相似文献
11.
This paper is concerned with a cubic Kolmogorov system with a parabolicsolution which does not contact and intersect the coordinates. The conclusionis that such a system may possess limit cycles. 相似文献