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LoNG TIME ASYMpToTIC BEHAVIoR oF SoLUTIoN oF DIFFERENCE SCHEME FoR A SEMILINEAR pARABoLIC EQUATIoN (Ⅱ)

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Journal of computational mathematics 1998年第5期16卷 571-576页

作者： Hui Feng(Shenzhen University Normal College, Shenzhen 518060, china Laboratorp of computational physics, institute of applied physics and computational mathematics,p.o.box 8009, beijing 100088, china )Long-jnn Shen(Laboratory of computational physics, In 深圳大学师范学院广东深圳

In this paper we prove the solution of explicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the relevant nonlinear stationary problem as t→∞. For nonlinear parabolic problem, we obtain the long time asymptotic behavior of its discrete solution which is analogous to that of its continuous solution. For simplicity, we discuss one-dimensional problem.

关键词： Asymptotic behavior Explicit difference scheme Semilinear parabolic equation.

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 100088,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

GENERAL DIFFERENCE SCHEMES WITH INTRINSICpARALLELISM FoR SEMILINEAR pARABoLIC SYSTEMS oFDIVERGENCE TYpE

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Journal of computational mathematics 1999年第4期17卷 337-352页

作者： Yu-lin Zhou Guang-wei Yuan(Laboratory of computational physics, Center of Nonlinear Studies, institute of applied physics and computational mathematics, p.o. box 8009, beijing 100088, china) Laboratory of computational physics Center of Nonlinear Studies Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.

关键词： difference scheme intrinsic parallelism semilinear parabolic system convergence

oN THE CoUpLING oF BoUNDARY INTEGRAL AND FINITE ELEMENT METHoDS FoR SIGNoRINI pRoBLEMS

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Journal of computational mathematics 1998年第6期16卷 561-570页

作者： Wei-jun Tang Hong-yuan Fu Long-jun Shen(Laboratory of computational physics, institute of applied physics and computational mathematics, p.o. box 8009, beijing 100088, china) 北京应用物理和计算数学所北京

In this paper, a exterior Signorini problem is reduced to a variational inequality on a bounded inner region with the help of a coupling of boundary integral and finite element methods. We established a equivalence between the original exterior Signorini problem and the variational inequality on the bounded inner region coupled with two integral equations on an auxiliary boundary. We also introduce a finite element approximation of the variational inequality and a boundary element approximation of the integral equations. Furthermore, the optimal error estimates are given.

关键词： boundary element finite element Signorini problems

THE UNCoNDITIoNAL STABLE DIFFERENCE METHoDS WITH INTRINSIC pARALLELISM FoR TWo DIMENSIoNAL SEMILINEAR pARABoLIC SYSTEMS

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Journal of computational mathematics 2003年第1期21卷 63-70页

作者： Guangwei Yuanf Longjun Shen(National Laboratory of computational physics, institute of applied physics and computational mathematics, p.o. box 8009, beijing, 100088, china) Ningbo University institute of applied physics and computational mathematics P.O. Box 8009 National Laboratory of Computational Physics 北京 100088

In this paper we are going to discuss the difference schemes with intrinsic parallelism for the boundary value problem of the two dimensional semilinear parabolic systems. The unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete w2(2,1)norms. Then the uniqueness of the discrete vector solution of this difference scheme follows as the consequence of the stability.

关键词： Difference Scheme Intrinsic parallelism Two Dimensional Semilinear parabolic System Stability.

Weak Morrey spaces and strong solutions to the Navier-Stokes equations

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Science china mathematics 2007年第10期50卷 1401-1417页

作者： Chang-xing MIAo~(1+) Bao-quan YUAN~2 ~1 institute of applied physics and computational mathematics,p.o.box 8009,beijing 100088,china ~2 College of mathematics and Informatics,Henan polytechnic University,Jiaozuo 454000,china institute of applied physics and computational mathematics Beijing China College of mathematics and Informatics Henan Polytechnic University Jiaozuo China

We consider the Cauchy problem of Navier-Stokes equations in weak Morrey *** first define a class of weak Morrey type spaces M_(p,λ)~*(R^n)on the basis of Lorentz space L_(p,∞)=L_p~*(R^n) (in particular,M_(?)~*(R^n)=L_(p,∞),if p>1),and study some fundamental properties of them;Second, we prove that the heat operator U(t)= e^(tΔ)and Calderón-Zygmund singular integral operators are bounded linear operators on weak Morrey spaces,and establish the bilinear estimate in weak Morrey ***,by means of Kato's method and the contraction mapping principle,we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces M_(p,λ)~*(R^n)(1p≤n)is time-global well-posed,provided that the initial data are sufficiently ***,we also obtain the existence and uniqueness of the serf-similar solution for Navier-Stokes equations in these spaces,because the weak Morrey space M_(p,n-p)~*(R^n)can admit the singular initial data with a self-similar *** this paper generalizes Kato's results.

关键词： Navier-Stokes equations, weak Morrey spaces, Lorentz spaces, Cauchy problem,time-global well-posedness, self-similar solutions

Dielectronic Recombination Rate Coefficients for Nickel-like Ytterbium

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Chinese Journal of Lasers 1996年第3期B5卷 242-247页

作者： ZHAo Libol LI Shichang(institute of physics, Academic Sinica, p. o. box 603, beijing 100080,institute of applied physics and computational mathematics, p. o. box 8009, beijing, china) Inst of physics Academia Sinica Beijing China

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关键词： dielectronic recombination autoionizing state Auger rate

Long-Time Behaviour of the Solutions for the Multidimensional Kolmogorov-Spieqel-Sivashinsky Equation

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Acta Mathematica Sinica,English Series 2002年第3期18卷 579-596页

作者： Bo Ling GUo Bi xiang WANG institute of applied physics and computational mathematics, p. o. box 8009. beijing 100088. p. R. china institute of applied physics and computational mathematics Beijing P. R. China

In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the esti- mates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the Gevrey class regularity for the solutions and construct an approximate inertial manifold for the system.

关键词： Global solution Approximate inertial manifold Gevrey class regularity Kolmogorov-Spiegel-Sivashinsky equation

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,100088,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