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Numerical Solution of Kortweg-de Vries Equation

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Applied math.matics 2020年第4期11卷 344-362页

作者： Fakhirah Alotaibi M. S. Ismail dept. of math King Abdulaziz University Jeddah Saudi Arabia

In this paper, we are going to derive numerical methods for solving the KdV equation using Pade approximation for space direction, trapezoidal and implicit mid-point rule in the time direction. The schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities will be used to display the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be conducted. The numerical results showed, interaction behavior is elastic and the conserved quantities are conserved which is a good indication of the reliability of the schemes under consideration.

关键词： KdV Soliton Pade Approximation Numerical Schemes Interaction of Solitons

The Vertex Euclidean Properties of Graphs

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Acta math.matica Sinica,English Series 2022年第7期38卷 1185-1202页

作者： Zhen Bin GAO Meng WANG Sin Min LEE Harris KWONG Shu Juan WANG College of math.matical Sciences Harbin Engineering UniversityHarbin 150001P.R.China 1786 Plan Tree Drive UplandCA 91784USA dept.of math.Sci. SUNY FredoniaFredoniaNY 14063USA

A simple graph G=(V,E)is said to be vertex Euclidean if there exists a bijection f from V to{1,2,...,|V|}such that f(u)+f(v)>f(w)for each C3 subgraph with vertex set{u,v,w},where f(u) 详细信息

A simple graph G=(V,E)is said to be vertex Euclidean if there exists a bijection f from V to{1,2,...,|V|}such that f(u)+f(v)>f(w)for each C3 subgraph with vertex set{u,v,w},where f(u)

关键词： Vertex Euclidean graph vertex Euclidean deficiency total graph of simple graph Zykov graph

NUMBER OF BOUNDED SOLUTIONS IN CRITICAL CASE

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Annals of Differential Equations 2002年第4期18卷 352-360页

作者：黄振坤 dept. of math Teachers College Jimei University Xiamen 360010

In this paper, using the method of linearization, we determine the number of bounded solutions of ordinary differential equations in critical case.

关键词： number bounded solution critical case

ON THE W^1,q ESTIMATE FOR WEAK SOLUTIONS TO A CLASS OF DIVERGENCE ELLIPTIC EQUATIONS

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Journal of Partial Differential Equations 2002年第1期15卷 7-12页

作者：周树清邓松海等 Wuhan Inst of Physics and math.Chinese Acad Sci. Wuhan 430071 dept. of math.of Hunan Norm. Univ. Changsha 410081 China dept. of math.of Xiangya Med. Inst. in Mid-east Univ. Changsha 410078 China dept. of math.of Hunan Norm. Univ. Changsha 410081 China

Local W1,q estimates for weak solutions to a class of equations in divergence formDi (aij (x)|Du|p-2Dju) = 0are obtained, where q ＞ p is given. These estimates are very important in obtaining higher regularity for th... 详细信息

关键词：弱解局部W^1,q估计发散椭圆型方程 Dirichlet问题

A CRITICAL VALUE FOR GLOBAL NONEXISTENCE OF SOLUTION OF A WAVE EQUATION

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Journal of Partial Differential Equations 2005年第3期18卷 263-266页

作者： Cao Zhenchao dept. of math Xiamen Univ Xiaman 361005 China

Consider the Cauchy problem for a wave equation on R^2： utt - △u =｜u｜^p-1u. In 1981 Glassey gave a guess to a critical value p（2） =1/2 （3 ＋√17）： when p 〉 p（2） there may exist a global solution and when 1 〈 p 〈 p（2） the solution may blow up. By our main result in this paper a counter example to the guess is given that the solution may also blow up in finite time even if p（2）〈 p 〈 5.

关键词： Wave equation global nonexistence a guess to critical value.

OSCILLATION IN FIRST ORDER NEUTRAL DIFFERENTIAL EQUATIONS

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Annals of Differential Equations 2003年第3期19卷 334-336页

作者：林诗仲 dept. of math . Hainan Normal University Haikou 571158

A new oscillation result is established for the first order neutral differential equationx(t) - px(t - (?)) + qx(t - σ) = 0.The results extends and improves some existing results in the literature.

关键词： neutral difFerential equation characteristic equation oscillation

A CLASS OF STRONGLY NONLINEAR SINGULARLY PERTURBED INTERIOR LAYER PROBLEMS

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Annals of Differential Equations 2004年第3期20卷 278-282页

作者：唐荣荣 dept.of math. Huzhou Teachers CollegeHuzhou 313000n this paper a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained.

In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained.

关键词： singular perturbation interior layer problems differential inequality asymptotic behavior

Bin-objective shape optimization based on linear programming model of arch dam

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Journal of Harbin Institute of Technology(New Series) 2007年第3期14卷 436-439页

作者：金海林皋阳明盛 School of Architecture and Civil Engineering Xiamen University School of Civil Eng.and Archit. Dalian Univ.of Technol. dept.of Appl.math. Dalian Univ.of Technol.

Bin-objective shape optimization of arch dam based on linear programming model is discussed to minimize both dam volume and maximal tensile *** importance of weight coefficient of the above two objectives is chosen according to the value of importance *** influence of weight coefficient to the optimization result is discussed in detail and the numerical example shows that both the model and method proposed is doable.

关键词： optimization arch dam linear programming bin-objective

RECENT DEVELOPMENTS IN THE OSCILLATION OF NEUTRAL DELAY DIFFERENCE EQUATIONS WITH SUMMABLE COEFFICIENTS

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邵阳学院学报（社会科学版） 1998年第2X期 1-5页

作者：王志成 math.dept. Hunan Univ.Cbangsha 410082 China

This paper surveys some new results on the oscillation of all solutions of the linear nentral delaydifference equation of the form △(yn - pnyn-k) + qnyn-l = 0, n = 0,1, 2…where { pn } and { qn } are twe real numbers sequences with qn≥0, and k and l are positive integers. These re-sults do not require the usual assumptionAlso, some interesting open problems on this topic am given.

关键词： Delay difference equation oscillation summable coefficient