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New Jacobian Elliptic Function Solutions to Modified KdV Equation: Ⅰ

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Communications in Theoretical Physics 2002年第8期38卷 143-146页

作者： YAN Zhen-Ya department of applied mathematics Dalian University of Technology Dalian 116024 China

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations.

关键词： modified KdV equation, Jacobian elliptic function, solitary wave solution, trigonometric functionsolution

THE FLOW PROBLEM OF FLUIDS FLOW IN A FRACTAL RESERVOIR WITH DOUBLE POROSITY

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applied mathematics and Mechanics(English Edition) 2001年第10期22卷 1118-1126页

作者： TONG Deng-ke(同登科) Zhang Hong-qing(张鸿庆) department of applied mathematics Petroleum University East of China Dongying 257061 P R China Institute of Mathematical Science Dalian University of TechnologyDalian 116024 P R China

The effective radius of oil well is introduced in the inner boundary in the problem of fluids flow through fractal reservoir with double porosity, and thus a new model is established. Taking the wellbore storage and steady-state skin effect into consideration, the exact solutions of the pressure distribution of fluids flow in fractal reservoirs with double porosity are given for the cases of an infinite outer boundary, a finite closed outer boundary and a bounded domain with the constant pressure outer boundary conditions. The pressure behavior of fractal reservoir with double porosity is analyzed by using a numerical inversion of the Laplace transform solution. The pressure responses of changing various parameters are discussed.

关键词： fractal double porous media seepage well test analysis

AN OPTIMAL MODEL AND ITS IDENTIFICATION FOR THE THERMODYNAMICS OF KEROGEN EV

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applied mathematics(A Journal of Chinese Universities) 1994年第3期9卷 307-313页

作者：冯恩民王秀梅 department of applied mathematics Dalian University of Technology Dalian

In this paper, a mathematical model with respect to the optimalidentification of the thermodynamic parameters is established. The identifiabitity of the dynamics problem is proved and necessary conditions of the optim... 详细信息

关键词： 1991 MR Subject Classification: 49J15, 49K15 Identification kerogen thermal degradation thermodynamics parameters

EXACT SOLUTION AND ITS BEHAVIOR CHARACTERISTIC OF NONLINEAR DUAL-POROSITY MODEL

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applied mathematics and Mechanics(English Edition) 2005年第10期26卷 1277-1283页

作者：同登科张鸿庆王瑞和 College of mathematics and Computational Science China University of Petroleum Dongying 257061 Shandong Province P.R.China department of applied mathematics Dalian University of Technology Dalian 116024 P.R.China

A nonlinear dual-porosity model considering a quadratic gradient term is presented. Assuming the pressure difference between matrix and fractures as a primary unknown, to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the blocks from the fractures was furnished with a quasi-steady-state flow in the blocks. Analytical solutions were obtained in a radial flow domain using generalized Hankel transform. The real value cannot be gotten because the analytical solutions were infinite series. The real pressure value was obtained by numerical solving the eigenvalue problem. The change law of pressure was studied while the nonlinear parameters and dual-porosity parameters changed, and the plots of typical curves are given. All these result can be applied in well test analysis.

关键词： nonlinear dual porosity Hankel transform analytical solution pressure cuI've

Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

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Acta Mathematicae Applicatae Sinica 2008年第1期24卷 29-40页

作者： Chun-fa Li Xue Yang En-min Feng School of Management Tianjin University of Technology Tianjin 300191 China School of Management Tianjin University Tianjin 300072 China department of applied mathematics Dalian University of Technology Dalian 116024 China

In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.

关键词： Distributed parameter system strong variation method optimal control adjoint system semilinear parabolic equations

A Series of Soliton-like and Double-like Periodic Solutions of a (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

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Communications in Theoretical Physics 2004年第11期42卷 655-660页

作者： CHEN Yong,~(1,3,4, WANG Qi~(2,4) LI Biao~(2,4) ~1department of mathematics,Ningbo university,Ningbo 315211,China ~2department of applied mathematics,dalian university of Technology,dalian 116024,China ~3department of Physics,Shanghai Jiao Tong university,Shanghai 200030,China ~4Key Laboratory of mathematics Mechanization~ the Chinese Academy of Sciences,Beijing 100080,China department of mathematics Ningbo University Ningbo 315211 China department of Physics Shanghai Jiao Tong University Shanghai 200030 China Key Laboratory of mathematics Mechanization the Chinese Academy of Sciences Beijing 100080 China department of applied mathematics Dalian University of Technology Dalian 116024 China

We generalize the algebraic method presented by Fan [***.A:***.36 (2003) 7009)] to uniformlyconstruct a series of soliton-like solutions and double-llke periodic solutions for nonlinear partial differential equations(NPDE),As an application of the method,we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equa-tion and successfully construct new and more general solutions including a series of nontraveling wave and coefficientfunctions’ soliton-like solutions,double-like periodic and trigonometric-like function solutions.

关键词： symbolic computation soliton-like solution Weierstrass and Jacobi elliptic functions periodic solution

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applied mathematics and Mechanics(English Edition) 2002年第4期23卷 380-386页

作者：谢福鼎闫振亚张鸿庆 department of applied mathematics Dalian University of Technology Dalian P R China

Four families of similarity reductions are obtained for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem via using both the direct method due to Clarkson and Kruskal and the improved direct met... 详细信息

关键词： nonlinear evolution equation FPU problem similarity reduction

Nonlinear Vibration Analyses of Cylindrical Shells Composed of Hyperelastic Materials

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Acta Mechanica Solida Sinica 2019年第4期32卷 463-482页

作者： Jing Zhang Jie Xu Xuegang Yuan Hu Ding Datian Niu Wenzheng Zhang College of mathematics and Information North Minzu UniversityYinchuan 750021China School of Science Dalian Minzu UniversityDalian 116600 China State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsDalian University of TechnologyDalian 116024China Shanghai Institute of applied mathematics and Mechanics Shanghai UniversityShanghai 200072China

The nonlinear vibration problem is studied for a thin-walled rubber cylindrical shell composed of the classical incompressible Mooney-Rivlin material and subjected to a radial harmonic excitation. With the KirchhofF-Love hypothesis, DonnelFs nonlinear shallow shell theory, hyperelastic constitutive relation, Lagrange equations and small strain hypothesis, a system of nonlinear differential equations describing the large-deflection vibration of the shell is derived. First, the natural frequencies of radial, circumferential and axial vibrations axe studied. Then, based on the bifurcation diagrams and the Poincare sections, the nonlinear behaviors describing the radial vibration of the shell are illustrated. Examining the influences of structural and material parameters on radial vibration of the shell shows that the vibration modes are highly sensitive to the thickness-radius ratio when the ratio is less than a certain critical value. Moreover, in terms of the results of multimodal expansion, it is found that the response of the shell to radial motion is more regular than that without considering the coupling between modes, while there are more phenomena for the uncoupled case.

关键词： Thin-walled cylindrical shell Incompressible Mooney-Rivlin material Donnell5s nonlinear shallow shell theory Nonlinear vibration

On Types of Isolated KKT Points in Polynomial Optimization

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Journal of Systems Science & Complexity 2023年第5期36卷 2186-2213页

作者： GUO Feng JIAO Liguo KIM Do Sang PHAM Tien-Son School of Mathematical Sciences Dalian University of TechnologyDalian 116024China Academy for Advanced Interdisciplinary Studies Northeast Normal UniversityChangchun 130024China department of applied mathematics Pukyong National UniversityBusan 48513South Korea department of mathematics Dalat UniversityDalat 96300Vietnam.

Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in R^(n).In this paper,the authors are interested in the problem of identifying the type(local minimizer,maximizer or not extremum point)of a given isolated KKT point x^(*)of f over *** this end,the authors investigate some properties of the tangency variety of f on S at x^(*),by which the authors introduce the definition of faithful radius of f over S at x^(*).Then,the authors show that the type of x^(*)can be determined by the global extrema of f over the intersection of S and the Euclidean ball centered at x^(*)with a faithful ***,the authors propose an algorithm involving algebraic computations to compute a faithful radius of x*and determine its type.

关键词： Faithful radii KKT points polynomial functions tangency varieties types