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Finite Dimensional Behavior of Global Attractors for Weakly Damping Ginzburg-Landau Equations Coupling with BBM Equations

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Communications in Nonlinear Science and Numerical Simulation 1998年第1期3卷 10-14页

作者： Boling GUO * and Murong JIANG + *(institute of applied {2. and computational {4.,Beijing,100088,china) +(Department of {4.,Yunnan University,Kunming 650091,china) E mail:guobl@*** Inst. Appl. Phys. and Compl. Math. Beijing 100088 China Department of mathematics Yunnan University Kunming 650091 China

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅａｒｅｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｌｏｎｇｔｉｍｅｂｅｈａｖｉｏｒｏｆｓｏｌｕｔｉｏｎｓｏｆｔｈｅｆｏｌｏｗｉｎｇｐｅｒｉｏｄｉｃｉｎｉｔｉａｌｖａｌｕｅｐｒｏ... 详细信息

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅａｒｅｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｌｏｎｇｔｉｍｅｂｅｈａｖｉｏｒｏｆｓｏｌｕｔｉｏｎｓｏｆｔｈｅｆｏｌｏｗｉｎｇｐｅｒｉｏｄｉｃｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｆｏｒｔｈｅｓｙｓｔｅｍｏ...

关键词： dimension attractor Ginzburg Landau equation couped BBM equationIntroduction

Radiation mean free path for non-LTE fully ionized medium

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Nuclear Science and Techniques 1998年第3期9卷 129-133页

作者： Zhang Jun ( institute of applied {2. and computational {4., Beijing100088) institute of applied {2. and computational {4. Beijing 100088 China

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒａｄｉａｔｉｏｎｍｅａｎｆｒｅｐａｔｈ（ＲＭＦＰ）［１，２］ｉｓａｖｅｒｙｉｍｐｏｒｔａｎｔｐｈｙｓｉｃａｌｐａｒａｍｅｔｅｒｉｎｃａｌｃｕｌａｔｉｏｎｓｏｆｒａｄｉａｔｉｏｎｈｙｄ... 详细信息

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒａｄｉａｔｉｏｎｍｅａｎｆｒｅｐａｔｈ（ＲＭＦＰ）［１，２］ｉｓａｖｅｒｙｉｍｐｏｒｔａｎｔｐｈｙｓｉｃａｌｐａｒａｍｅｔｅｒｉｎｃａｌｃｕｌａｔｉｏｎｓｏｆｒａｄｉａｔｉｏｎｈｙｄｒｏｄｙｎａｍｉｃｓａｎｄｔｒａｎ...

关键词：等离子体流体力学辐照平均自由路径非定域热平衡

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 {2. and {4. mathematics,P.O.Box 8009,Beijing 100088,china ~2.College of mathematics and Informatics,Henan Polytechnic University,Jiaozuo 4.4.00,china institute of applied {2. and computational {4. 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)(1

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

H~m convergence rates of solutions of GBBM equations in multi-dimensional spaces

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Progress in Natural Science:Materials International 2009年第9期19卷 1053-1057页

作者： Shaomei Fang a,*, Boling Guo b a Department of mathematics, South china Agricultural University, Guangzhou 51064.2} china b {4. of applied physics and computational mathematics, Beijing 100088, china Department of mathematics South China Agricultural University Guangzhou 510642 China institute of applied {2. and computational {4. Beijing 100088 China

In this paper, we study the decay rates of the generalized Benjamin-Bona-Mahony equations in n-dimensional space. By using Fourier analysis for long wave and by applying the energy method for short wave, we obtain the Hm convergence rates of the solutions when the initial data are in the bounded subset of the phase space HmeRnTen P 3T. The optimal decay rates are obtained in our results and are found to be the same as the Heat equation.

关键词： Generalized Benjamin–Bona–Mahony equations Fourier analysis Energy method Optimal convergence rates

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 4.1105,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)

ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 421-432页

作者： SHU BIN (institute of applied {2. & physics, Shanghai Maritime University, Shanghai 2.0135, china.) institute of applied {2. and physics Shanghai Maritime University Shanghai 200135 China

In [2.], generalized restricted Lie algebras, defined over a field F of positive characteristic p, were introduced. In this note their cohomology, especially the so-called generalized restricted cohomology is studies. Some reduction properties are obtained. For graded Cartan type Lie algebras the author determines the first Lie-cohomology groups and the first generalized restricted cohomology groups with the coefficients in the highest weight modules from which all irreducible generalized restricted modules are derived.

关键词： Generalized restricted Lie algebras Generalized restricted Cohomology Lie algebras of Cartan type

Acoustic Impedance Inversion Via Wavelet Transform Constraints

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Communications in Nonlinear Science and Numerical Simulation 1998年第1期3卷 3-5页

作者： Huiyan ZHANG and Bainian LU (Graduate School, Research institute of Petrolem Expl. & Dev. Beijing,100083,china) +(institute of computational and {4. mathematics, Xiangtan University, 4.1105, china) *(institute of {4. physics Graduate School Research Institute of Petrolem Expl. & Dev. Beijing 100083 China institute of computational and {2. mathematics Xiangtan University Xiangtan 411105 China institute of applied {2. and computational {4. Beijing 100088 China Graduate School of china Academy of Engineering physics Beijing 100088 China

ＩｎｔｒｏｄｕｃｔｉｏｎＷａｖｅｌｅｔｔｒａｎｓｆｏｒｍ，ＷＴ，ｔｈｅｏｒｙｈａｓｄｅｖｅｌｏｐｅｄｒａｐｉｄｌｙｄｕｒｉｎｇｔｈｅｌａｓｔｆｅｗｙｅａｒｓａｎｄｈａｓｂｅｅｎｓｕｃｃｅｓｆｕｌｙａｐｐｌｉｅｄｉｎｍ... 详细信息

ＩｎｔｒｏｄｕｃｔｉｏｎＷａｖｅｌｅｔｔｒａｎｓｆｏｒｍ，ＷＴ，ｔｈｅｏｒｙｈａｓｄｅｖｅｌｏｐｅｄｒａｐｉｄｌｙｄｕｒｉｎｇｔｈｅｌａｓｔｆｅｗｙｅａｒｓａｎｄｈａｓｂｅｅｎｓｕｃｃｅｓｆｕｌｙａｐｐｌｉｅｄｉｎｍａｎｙｄｉｆｅｒｅｎｔｆｉｅｌｄｓ...

关键词： acoustic impedance inversion wavelet transform priori scale information

Long time behavior for damped generalized coupled nonlinear wave equations. Ⅱ.Unbounded domain

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Communications in Nonlinear Science and Numerical Simulation 2001年第2期6卷 107-110页

作者： Shaomei FANG and Boling GUO Department of mathematics, Shaoguan University, Shaoguan 512.05, china Graduate School, china Academy of Engineering {4., Beijing 100088, china Center for Nonlinear Studies, institute of applied {4. and computational Department of mathematics Shaoguan University Shaoguan 512005 China Graduate School China Academy of Engineering Physics Beijing 100088 China Center for Nonlinear Studies Institute of Applied Physics and Computational mathematics Beijing 100088 China

In this paper, by using a priori estimates in the weighted space, the existence of the global attractor for the damped generalized coupled nonlinear wave equations in an unbounded domain is obtained.

关键词： unbounded domain weighted space attractor

Weak Periodic Solutions of Non-Newtonian Viscous Incompressible Fluids

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 56-60页

作者： Boling GUO* and Guoguang LTN** (institute of applied {2. and computational {4., Be1Jing 100088, china) and Guoguang LTN (Graduate School of china Academy of Engineering {2., Beijing 100088, china) + (Department of {4., Yunnan Univ Inst. Appl. Phys. and Compl. Math. Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China Department of mathematics Yunnan University Kunming 650091 China

The existence of weak periodic solution in time of non-Newtonian fluids with a time periodic forcing is established.

关键词： periodic solution weak periodic solution bipolar fluid