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On the Suitable Weak Solutions to the Boussinesq Equations in a Bounded Domain

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Acta Mathematica Sinica,English Series 1996年第2期12卷 205-216页

作者： Guo Boling Yuan Guangwei Guo Boling Yuan Guangwei institute of applied physics and computational mathematics beijing,{2.china institute of applied physics and computational mathematics

In this paper we construct the suitable weak solution for the initial-boundary value problem of the Boussinesq equations and obtain some properties for these *** in the case of a two dimensional space the uniqueness o... 详细信息

关键词： Initial-boundary value Existence Boussinesq equations

A REMARK ON THE GLOBAL SMALL SOLUTION FOR GENERAL COUPLED MAXWELL-SCHR■DINGER EQUATIONS IN IR^3

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Systems Science and Mathematical Sciences 1999年第2期12卷 97-103页

作者： MIAO Changxing(institute of applied physics and computational mathematics, beijing 1.0088. china)LI Zemin(Department of {2., Zhengzhou University, Zhengzhou 450052. china)

This note is a continuation of earlier papers "The Cauchy Problem for General Coupled Maxwell-Schrodinger Equations (I) (II)". When the spatial dimensions are three ,we prove the existence of global small solution for... 详细信息

关键词： Coupled Maxwell-Schrodinger equations Cauchy problem quasi-energy method.

The Cauchy Problem of the Nonlinear Schr■dinger Equations in R1+1

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Acta Mathematicae Applicatae Sinica 2007年第4期 593-610页

作者： Gui-xiang Xu institute of applied physics and computational mathematics,P.O.Box 8009,beijing {2.china

In this paper,we consider the local and global solution for the nonlinear Schrdinger equationwith data in the homogeneous and nonhomogeneous Besov space and the scattering result for small *** to be used are adapted from the Strichartz type estimate,Kato’s smoothing effect and the maximalfunction(in time)estimate for the free Schrdinger operator.

关键词： Schrdinger equation cauchy problem besov space littlewood-paley decomposition self-similar solution

Attractors and Dimensions for Discretizations of a Dissipative Zakharov Equations

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Acta Mathematicae Applicatae Sinica 2002年第2期18卷 201-214页

作者： Qian-shun Chang, Bo-ling Guoinstitute of applied {2., Academy of {2. and System Sciences, Chinese Academy of Sciences,beijing 100080, chinainstitute of applied physics and computational mathematics, beijing 1.0088. china institute of applied {2. Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China institute of applied physics and computational mathematics Beijing China

In this paper, a dissipative Zakharov equations are discretized by difference method. We make prior estimates for the algebric system of equations. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds of the Hausdorff dimensions of the discrete attractors are obtained, and the various bounds are dependent of the mesh sizes.

关键词： Attractor dissipative Zakharov equation

New progress in the principle of nonequilibrium statistical physics

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Chinese Science Bulletin 2001年第6期46卷 448-454页

作者： XING XiusanDepartment of applied physics, {2. institute of Technology, {2. 100081, china Department of applied physics Beijing Institute of Technology Beijing China

In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but does not obey the Newton equation of motion, though it is also constrained by dynamics. The stochastic diffusion of the particles is the microscopic origin of macroscopic irre-versibility. Starting from this equation, the BBGKY diffusion equation hierarchy was presented, the hydrodynamic equations, such as the generalized Navier-Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified description of all three level equations of microscopic, kinetic and hydrodynamic

关键词： anomalous Langevin equation in space drift-diffusion duality stochastic law nonequilibrium entropy evolution equation entropy diffusion.

Exponential Attractors for the Generalized Ginzburg-Landau Equation

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Acta Mathematica Sinica,English Series 2000年第3期16卷 515-526页

作者： Boling Guo institute of applied physics and computational mathematics P.O.Box 8009,beijing,{2.P.R.chinaBixiang Wang Department of mathematics,Brigham Young University,Provo,UT84602.USA institute of applied physics and computational mathematics Bejing 100088 P. R. China Department of mathematics Brigham Young University Provo UT 84602 USA

In this paper,we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial *** show the squeezing property and the existence of fimte dimen- sional exponential attractors for this e... 详细信息

关键词： Global attractor Exponential attractor Semigroup Ginzburg-Landau equation

Economical cascadic multigrid method (ECMG)

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Science china mathematics 2007年第12期50卷 1765-1780页

作者： Zhong-ci SHI~1 Xue-jun XU~(1+) Yun-qing HUANG~2.~1 LSEC,institute of computational {2.,Academy of {2. and Systems Science,Chinese Academy of Sciences,beijing 100080,china ~2.Hunan Key laboratory for Computation and Simulation in Science and Engineering,institute for computational and applied {2.,Xiangtan University,Xiangtan 411105,china LSEC Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Hunan Key laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan China

In this paper, an economical cascadic multigrid method is proposed. Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard, the new one requires less iterations on each level, especially on the coarser grids. Many operations can be saved in the new cascadic multigrid algorithms. The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations. The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough. A new formulae of the error reduction rate is employed in our new algorithm. Numerical experiments are reported to support our theory.

关键词： economical cascadic multigrid method (ECMG), cascadic multigrid method (CMG)

Calculation of Atomic Structurefor Arbitrary Temperature andMatter Density

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计算物理 1993年第1期 55-61页

作者： Sun Yongsheng, Meng Xujun,and Li Shichanginstitute of applied physics and computational mathematics P. O.Box 8009 beijing, {2.china

Schrodinger wave equation is solved for arbitrary matter density and temperature in the Hartree - Fock-Slater (HFS) self-consistent field method. In order to describe relativistic effects, the mass -velocity, the Darwin and spin -orbit coupling terms are included in the wave equation. Some of our results are compared with experimental data and with other theoretical model, the present results are consistent with experiment better and are close to that of Reference.

关键词： atomic structure self-consitent field temperature and density

A SECOND ORDER DIFFERENCE SCHEME WITH NONUNIFORM MESHES FOR NONLINEAR PARABOLIC SYSTEM

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Journal of Systems Science & Complexity 2003年第2期16卷 199-208页

作者： WANZhengsu CHENGuangnan Departmentofmathematics ShanghaiUniversityShanghai200436China laboratoryofcomputational{2. InstituteofAppliedPhysicsandComputationalMathematicsP.O.Box8009Beijing100088China

In this paper, a difference scheme with nonuniform meshes is established for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in spaces... 详细信息

关键词： second order difference nonuniform meshes