共查询到19条相似文献,搜索用时 62 毫秒
1.
In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method. 相似文献
2.
The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions. 相似文献
3.
Guochun Wen 《分析论及其应用》2005,21(2):118-131
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order. 相似文献
4.
Guo Chun Wen 《数学学报(英文版)》2013,29(12):2233-2244
In this article, we first transform the general uniformly elliptic systems of first order equations with certain conditions into the complex equations, and propose the discontinuous Riemann- Hilbert problem and its modified well-posedness for the complex equations. Then we give a priori estimates of solutions of the modified discontinuous Riemann-Hilbert problem for the complex equations and verify its solvability. Finally the solvability results of the original discontinuous Riemann-Hilbert boundary value problem can be derived. The discontinuous boundary value problem possesses many applications in mechanics and physics etc. 相似文献
5.
谭绍滨 《应用数学学报(英文版)》1993,(4)
In this paper we consider the semi-discretization difference method for the system of Zakharov equations.Under certain conditions,the convergence,error stimates and stability of the given difference scheme are studied. 相似文献
6.
EXACT TRAVELING WAVE SOLUTIONS OF MODIFIED ZAKHAROV EQUATIONS FOR PLASMAS WITH A QUANTUM CORRECTION*
In this article,the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method,hyperbolic seca... 相似文献
7.
Guo Chun Wen 《数学学报(英文版)》2008,24(11):1759-1774
The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains. 相似文献
8.
闻国椿 《数学物理学报(B辑英文版)》2007,27(3):663-672
The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved. 相似文献
9.
Qian-shun Chang Bo-ling GuoInstitute of Applied Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing ChinaInstitute of Applied Physics Computational Mathematics Beijing China 《应用数学学报(英文版)》2002,18(2):201-214
Abstract In this paper, a dissipative Zakharov equations are discretized by difference method.We make priorestimates for the algebric system of equations. It is proved that for each mesh size,there exist attractors forthe discretized system.The bounds of the Hausdorff dimensions of the discrete attractors are obtained,and thevarious bounds are dependent of the mesh sizes. 相似文献
10.
In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained. 相似文献
11.
Jun-Du Liang 《计算数学(英文版)》1984,2(4):364-375
This paper is intended to study the finite difference method for the periodic boundary and initial value problem of a class of system of generalized Zakharov equations. 相似文献
12.
A. B. Shabat 《Theoretical and Mathematical Physics》1999,121(1):1397-1408
The two previous versions of the dressing method in soliton theory were elaborated in collaboration with V. E. Zakharov. In
our works published in the 1970s, we did not consider discrete equations on a lattice Painlevé-type equations, and finite-band
potentials, and I now make up for this gap. Although the suggested elementary discretization scheme for the linear spectral
problem is rather general, the presentation of the material is mainly confined to the framework of the Zakharov-Shabat spectral
problem.
Dedicated to the 60th birthday of V. E. Zakharov
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 1, pp. 165–176, October, 1999. 相似文献
13.
In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method. 相似文献
14.
郭柏灵 《应用数学学报(英文版)》1994,10(4):419-433
ONGLOBALSOLUTIONFORACLASSOFSYSTEMSOFMULTI-DIMENSIONALGENERALIZEDZAKHAROVTYPEEQUATIONGUOBOLING(郭柏灵)(InstituteofAppliedandCompu... 相似文献
15.
This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in (2+1) dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method. 相似文献
16.
17.
Soichiro Katayama 《Mathematische Zeitschrift》2012,270(1-2):487-513
We consider the Cauchy problem for coupled systems of wave and Klein–Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coupled system. Consequently our result is applicable to certain physical systems, such as the Dirac–Klein–Gordon equations, the Dirac–Proca equations, and the Klein–Gordon–Zakharov equations. 相似文献
18.
19.
A.H. Bhrawy M.A. Abdelkawy Anjan Biswas 《Communications in Nonlinear Science & Numerical Simulation》2013,18(4):915-925
This paper studies two nonlinear coupled evolution equations. They are the Zakharov equation and the Davey–Stewartson equation. These equations are studied by the aid of Jacobi’s elliptic function expansion method and exact periodic solutions are extracted. In addition, the Zakharov equation with power law nonlinearity is solved by traveling wave hypothesis. 相似文献