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EXISTENCE OF GLOBAL SMOOTH SOLUTION TO INITIAL BOUNDARY VALUE PROBLEM FOR A VISCOELASTIC MODEL WITH RELAXATION

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Acta Mathematica Scientia 2004年第2期24卷 265-274页

作者：阮立志朱长江 laboratoryofnonlinearanalysis Dept.ofMath.CentralChinaNormalUniversityWuhan430079China

This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the C^1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the 'maximum principle' of first-order quasilinear hyperbolic system.

关键词： Viscoelastic model relaxation a priori estimates maximum principle

Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation

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Acta Mathematicae Applicatae Sinica 2005年第1期21卷 31-42页

作者： Mi-naJiang Yan-lingXu laboratoryofnonlinearanalysis DepartmentofMathematicsCentralChinaNormalUniversityWuhan430079China DepartmentofInformationandComputerScience CollegeofScienceHuazhongAgricultureUniversityVuhan430079China

We investigate the asymptotic behavior of solutions of the initial-boundaryvalue problem for the generalized BBM-Burgers equation u_t + f(u)_x = u_(xx) + u_(xxt) on the halfline with the conditions u(0, t) = u_–, u(∞, t) = u + and u_– < u_+, where the correspondingCauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, becauseof the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signsof the characteristic speeds f(u_±) of boundary state u_– = u(0) and the far fields states u_+ =u(∞). In all cases both global existence of the solution and asymptotic behavior are shown underthe smallness conditions.

关键词： BBM-Burgers equation stationary solution rarefaction wave a prioriestimate L^2-energy method

New Results on Global Rank Axioms of Poset Matroids

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Acta Mathematica Sinica,English Series 2005年第1期21卷 143-154页

作者： ShuChaoLI YanQinFENG laboratoryofnonlinearanalysis DepartmentofMathematicsCentralChinaNormalUniversityWuhan430079P.R.China//DepartmentofControlScienceandEngineeringHuazhongUniversityofScienceandTechnologyWuhan430074P.R.China DepartmentofMathematics NanjingUniversityNanjing210093P.R.China

An excellent introduction to the topic of poset matroids is due to ***, G. Nicoletti and L. Pezzoli. On the basis of their work, we have obtained the global rankaxioms for poset matroids. In this paper, we study the special integral function f and obtain a newclass of poset matroids from the old ones, and then we generalize this result according to theproperties of f. Almost all of these results can be regarded as the application of global rankaxioms for poset matroids. The main results in our paper have, indeed, investigated the restrictionof the basis of the poset matroid, and we give them the corresponding geometric interpretation.

关键词： Poset matroids Rank function Derivative function Combinatorial schemes

EXISTENCE OF GLOBAL SMOOTH SOLUTION TO JIN-XIN MODEL WITH LARGE INITIAL DATA

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Journal of Partial Differential Equations 2004年第2期17卷 163-172页

作者： RuanLizhi ZhangZhiyong DepartmentofAppliedMathematics CollegeofComputerScienceSouth-CentralUniversityForNationalitiesWuhan430074China laboratoryofnonlinearanalysis DepartmentofMathematicsCentralChinaNormalUniversityWuhan430079China

In this paper, Under the assumption that the relaxation time ε is sufficiently small, we prove the existence of the global smooth solution to the Cauchy problem for the Jin-Xin model without any smallness assumption for the initial *** analysis is based on some a priori estimates which are obtained by the method of characteristic and the maximum principle of first-order quasilinear hyperbolic system.

关键词：偏微分方程假想模型极大值原理

Reexploring the upper bound for the chromatic number of graphs

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Progress in Natural Science:Materials International 2004年第3期 84-86页

作者： LI Shuchao 1,2 * and MAO Jingzhong 1(1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 2. Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, China) laboratoryofnonlinearanalysis DepartmentofMathematicsCentralChinaNormalUniversityWuhan430079China DepartmentofControlScienceandEngineering HuazhongUniversityofScienceandTechnologyWuhan430074China

The upper bound of the chromatic number of simple graphs is explored. Its original idea comes from Coffman, Hakimi and Schmeichel, who recently studied the chromatic number of graphs with strong conditions. In this pa... 详细信息

关键词： chromatic number clique number.