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THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN
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作者 刘其林 莫嘉琪 《应用数学和力学》 EI CSCD 北大核心 2001年第10期1075-1080,共6页
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i... A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied. 展开更多
关键词 奇摄动 反应扩散方程 初始边值问题 算子理论 渐近性态
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A CLASS OF NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS 被引量:10
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作者 莫嘉琪 《Acta Mathematica Scientia》 SCIE CSCD 2003年第3期377-385,共9页
A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for... A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions. 展开更多
关键词 NONLINEAR reaction diffusion equation singular perturbation
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THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS 被引量:3
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作者 莫嘉琪 许玉兴 《Acta Mathematica Scientia》 SCIE CSCD 1997年第1期44-50,共7页
In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansio... In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained. 展开更多
关键词 differential inequality singular perturbation asymptotic expansion elliptic partial differential equation boundary value problem
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The Nonlinear Nonlocal Singularly Perturbed Problems for Elliptic Equations with Boundary Perturbation 被引量:3
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作者 莫嘉琪 姚静荪 《Journal of Shanghai Jiaotong university(Science)》 EI 2006年第1期104-106,112,共4页
The nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation was considered.Under suitable conditions,firstly,the outer solution of the original problem is obtai... The nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation was considered.Under suitable conditions,firstly,the outer solution of the original problem is obtained,secondly,using the stretched variable,the composing expansion method and the expanding theory of power series the boundary layer is constructed,finally,using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. 展开更多
关键词 NONLINEAR elliptic equation singular perturbation
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OSCILLATION THEOREMS FOR SECOND ORDER QUASILINEAR PERTURBED DIFFERENTIAL EQUATIONS 被引量:2
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作者 Jiang Jianchu Li Xiaopingof Math., Loudi Teachers’College, Loudi 417000. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第3期244-250,共7页
New oscillation criteria for the second order perturbed differential equation are presented. The special case of the results includes the corresponding results in previous papers, extends and unifies a number of known... New oscillation criteria for the second order perturbed differential equation are presented. The special case of the results includes the corresponding results in previous papers, extends and unifies a number of known results. 展开更多
关键词 OSCILLATION Riccati transformation Smarzewski inequality perturbed differential equations.
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STABILITY OF PERTURBED NEUTRAL DIFFERENTIAL EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS 被引量:1
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作者 Ye Haiping Gao GuozhuDept.of Appl.Math., Donghua Univ.,Shanghai 200051,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第3期267-272,共6页
In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero soluti... In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained. 展开更多
关键词 neutral equation uniform stability asymptotic stability perturbing term.
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Approximate Generalized Conditional Symmetries for Perturbed Evolution Equations 被引量:3
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作者 ZHANG Shun-Li WANG Yong LOU Sen-Yue 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第6期975-980,共6页
The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via th... The concept of approximate generalized conditional symmetry (AGCS) for the perturbed evolution equations is introduced, and how to derive approximate conditional invariant solutions to the perturbed equations via their A GCSs is illustrated with examples. 展开更多
关键词 perturbed evolution equation approximate generalized conditional symmetry approximate con ditional invariant solution
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THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN 被引量:1
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作者 LIU Qi-lin(刘其林) +1 位作者 MO Jia-qi(莫嘉琪) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第10期1192-1197,共6页
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i... A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied. 展开更多
关键词 singular perturbation reaction diffusion equation initial boundary value problem
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Classification and Approximate Solutions to Perturbed Nonlinear Diffusion-Convection Equations 被引量:2
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作者 WANG Yong ZHANG Shun-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第1期17-21,共5页
This paper studies the perturbed nonlinear diffusion-convection equation with source term via the approximate generalized conditional symmetry (A GCS). Complete classification of those perturbed equations which admi... This paper studies the perturbed nonlinear diffusion-convection equation with source term via the approximate generalized conditional symmetry (A GCS). Complete classification of those perturbed equations which admit certain types of AGCSs is derived. Some approximate invariant solutions to the resulting equations can also be obtained. 展开更多
关键词 perturbed nonlinear diffusion-convection equation approximate generalized conditional symme-try approximate invariant solution
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Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Two Parameters and Boundary Perturbation
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作者 CHE Guo-feng CHEN Hai-bo 《Journal of Donghua University(English Edition)》 EI CAS 2016年第6期888-893,共6页
A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with two parameters and boundary perturbation were considered.Under suitable conditions,the existence,uniquene... A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with two parameters and boundary perturbation were considered.Under suitable conditions,the existence,uniqueness and asymptotic behavior of solutions for the initial boundary value problems were studied.An example was also given to illustrate our main results. 展开更多
关键词 EXISTENCE asymptotic behavior reaction diffusion equation singular perturbation boundary perturbation
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Nonlinear singularly perturbed problems of ultra parabolic equations
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作者 林苏榕 莫嘉琪 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第10期1377-1381,共5页
A class of nonlinear singularly perturbed problem of ultra parabolic equations are considered. Using the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied.
关键词 ultra parabolic equation singular perturbation asymptotic behavior comparison theorem
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SINGULARLY PERTURBED METHODS IN THE THEORY OF OPTIMAL CONTROL OF SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS
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作者 田根宝 林宗池 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第8期713-719,共7页
In this paper, the various problems associaled with the optimal control of systemsgoverned by partial differential equations are introduced by using singularly perturbedmethods for analysis based on stale equations,... In this paper, the various problems associaled with the optimal control of systemsgoverned by partial differential equations are introduced by using singularly perturbedmethods for analysis based on stale equations, or the cost funtction and also stateequations defined in perturbed domains. 展开更多
关键词 optimal control perturbation techniques partial differential equations
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SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS
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作者 任景莉 葛渭高 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第12期1450-1455,共6页
A boundary value problems for functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower sol... A boundary value problems for functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems' solution are established. A uniformly valid asymptotic expansions of the solution is also given. 展开更多
关键词 singular perturbation functional differential equation boundary value problem uniformly valid asymptotic expansion
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Oscillation theorems for second-order nonlinear perturbed differential equations with damping
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作者 张蒙 宋国华 《Journal of Shanghai University(English Edition)》 CAS 2011年第6期510-516,共7页
A class of second-order nonlinear damped perturbed differential equations is considered and its oscillation theorems are studied.These theorems are more general and deal with the cases which are not covered by the kno... A class of second-order nonlinear damped perturbed differential equations is considered and its oscillation theorems are studied.These theorems are more general and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify some existing results.An example is given to verify the results. 展开更多
关键词 oscillation criteria perturbed differential equation integral averaging technique
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Symbolic and Graphical Computations of a Class of Slightly Perturbed Equations
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作者 Mohammed A. Sharaf Abdel-naby S. Saad Zainab A. Mominkhan 《Applied Mathematics》 2013年第5期817-824,共8页
In this paper, a class of slightly perturbed equations of the form F(x)= ξ -x+αΦ(x) will be treated graphically and symbolically, where Φ(x) is an analytic function of x. For graphical developments, we set up a si... In this paper, a class of slightly perturbed equations of the form F(x)= ξ -x+αΦ(x) will be treated graphically and symbolically, where Φ(x) is an analytic function of x. For graphical developments, we set up a simple graphical method for the real roots of the equation F(x)=0 illustrated by four transcendental equations. In fact, the graphical solution usually provides excellent initial conditions for the iterative solution of the equation. A property avoiding the critical situations between divergent to very slow convergent solutions may exist in the iterative methods in which no good initial condition close to the root is available. For the analytical developments, literal analytical solutions are obtained for the most celebrated slightly perturbed equation which is Kepler’s equation of elliptic orbit. Moreover, the effect of the orbital eccentricity on the rate of convergence of the series is illustrated graphically. 展开更多
关键词 SYMBOLIC Computation Small perturbATIONS GRAPHICAL Representations TRANSCENDENTAL equations
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A Series Approach to Perturbed Stochastic Volterra Equations of Convolution Type
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作者 Anna Karczewska Bartosz Bandrowski 《Advances in Pure Mathematics》 2015年第11期660-671,共12页
In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration ... In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration is used. Sufficient conditions for the existence of strong solution to the class of perturbed stochastic Volterra Equations of convolution type are given. Regularity of stochastic convolution is supplied, as well. 展开更多
关键词 STOCHASTIC Linear Volterra equatION perturbed equatION Strong SOLUTION Resolvent Mild SOLUTION STOCHASTIC CONVOLUTION SERIES Approach
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The Nonlinear Singularly Perturbed Problems for Elliptic Equations with Boundary Perturbation
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作者 莫嘉琪 张伟江 陈贤峰 《Northeastern Mathematical Journal》 CSCD 2007年第4期293-297,共5页
The nonlinear singularly perturbed problems for elliptic equations with boundary perturbation are considered. Under suitable conditions, by using the theory of differential inequalities the asymptotic behavior of solu... The nonlinear singularly perturbed problems for elliptic equations with boundary perturbation are considered. Under suitable conditions, by using the theory of differential inequalities the asymptotic behavior of solutions for the boundary value problems is studied. 展开更多
关键词 NONLINEAR elliptic equation singular perturbation boundary perturbation
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An Asymptotic-Fitted Method for Solving Singularly Perturbed Delay Differential Equations
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作者 Awoke Andargie Yanala Narsimha Reddy 《Applied Mathematics》 2012年第8期895-902,共8页
In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay diffe... In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the new equation, we introduced a fitting parameter and determined its value using the theory of singular Perturbation;O’Malley [1]. The three term recurrence relation obtained is solved using Thomas algorithm. The applicability of the method is tested by considering five linear problems (two problems on left layer and one problem on right layer) and two nonlinear problems. 展开更多
关键词 Asymptotic-Fitted Scheme Delay-Differential equations SINGULAR perturbATION Boundary Layer
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Approximate Solutions of Perturbed Nonlinear Schroedinger Equations
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作者 CHENG Xue-Ping YE Li-Jun LIN Ji 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2X期227-231,共5页
By applying Lou's direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the ... By applying Lou's direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations. 展开更多
关键词 direct perturbation method perturbed nonlinear Schroedinger equation approximate solution
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Exact Topological Soliton Solutions to the Strongly Perturbed Family of Sine-Gordon Type Equations
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作者 Stephen Johnson Essaid Zerrad +1 位作者 Sokratis Makrogiannis Jun Ren 《Journal of Applied Mathematics and Physics》 2019年第10期2401-2422,共22页
This paper uses the Ansatz method to solve for exact topological soliton solutions to sine-Gordon type equations. Single, double, and triple sine-Gordon and sine-cosine-Gordon equations are investigated along with dis... This paper uses the Ansatz method to solve for exact topological soliton solutions to sine-Gordon type equations. Single, double, and triple sine-Gordon and sine-cosine-Gordon equations are investigated along with dispersive and highly dispersive variations. After these solutions are found, strong perturbations are added to each equation and the new solutions are found. In solving both the perturbed and unperturbed sine-Gordon type equations, constraints are imposed on the parameters. The novel contributions of the authors are the soliton solutions to the strongly perturbed sine-Gordon equation and its variations. These results are important to the study of Josephson junctions, crystal dislocations, ultra-short optical pulses, relativistic field theory, and elementary particles. 展开更多
关键词 TOPOLOGICAL SOLITON KINK SOLITON SINE-GORDON equation Dispersion perturbATION
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