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Applied mathematics(A Journal of Chinese Universities) 2007年第2期22卷 201-206页

作者： mo jiaqi department of mathematics, anhui normal university, wuhu 24.000, china.department of mathematics,{4., huzhou 313000, china.division of computational science, E-Institutes of shanghai Universities at SJTU, shanghai 20024., china. department of mathematics Anhui Normal University Wuhu 241000 China

A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptoti... 详细信息

关键词： nonlinear reaction diffusion singular perturbation boundary perturbation

THE SOLVABILITY FOR A CLASS OF SINGULARLY PERTURBED QUASI-LINEAR DIFFERENTIAL SYSTEM

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Acta Mathematica Scientia 2008年第3期28卷 495-500页

作者：莫嘉琪王辉林万涛 department of Mathemtics Anhui Normal University division of computational science E-Institutes of Shanghai Universities at SJTUShanghai 200240China department of mathematics Huzhou Teachers'CollegeHuzhou 313000China Chinese Academy of Meteorological sciences LASG Institute of Atmospheric PhysicsChinese Academy of Sciences

The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using t... 详细信息

关键词： Solvability singular perturbation differential system boundary layer

Singularly Perturbed Solution of Coupled model in Atmosphere-ocean for Global Climate

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Chinese Geographical science 2008年第2期18卷 193-196页

作者： mo jiaqi LIN Wantao WANG Hui department of mathematics Anhui Normal University Wuhu 241000 China division of computational science E-Institutes of shanghai Universities at SJTU Shanghai 200240 China huzhou teachers college Huzhou 313000 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Chinese Academy ofMeteorological sciences Beijing 100081 China

A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global cli-mate is considered. By using the multi-scales method, the asymptotic solution of a simplified weakly nonlinear model is discussed. Firstly, by introducing first scale, the zeroth order approximate solution of the model is obtained. Sec-ondly, by using the multi-scales, the first order approximate equation of the model is found. Finally, second order ap-proximate equation is formed to eliminate the secular terms, and a uniformly valid asymptotic expansion of solution is decided. The multi-scales solving method is an analytic method which can be used to analyze operation sequentially. And then we can also study the diversified qualitative and quantitative behaviors for corresponding physical quantities. This paper aims at providing a valid method for solving a box model of the nonlinear equation.

关键词： atmosphere-ocean El Nino-Southern Oscillation singular perturbation approximate solution

Homotopic Mapping Solving Method for Perturbed Mechanism of Western Boundary Undercurrents in Equator Pacific

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Chinese Geographical science 2006年第4期16卷 347-350页

作者： mo jiaqi WANG Hui LIN Wantao department of mathematics Anhui Normal University Wuhu 241000 China division of computational science E-Instilutes of Shanghai Universities Shanghai Jiaotong University Shanghai 200240 China department of mathematics Huzhou Teachers College Huzhou 313000 China Chinese Academy of Meteorological sciences Beijing 100081 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China

The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment, but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-eogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value. It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.

关键词： undercurrent perturbation approximate solution equator Pacific

THE SOLVABILITY FOR HEAT CONDUCTIVE PROBLEM WITH BOUNDARY PERTURBATION

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Annals of Differential Equations 2007年第1期23卷 45-49页

作者： mo jiaqi Chen Xianfeng Xie Feng Dept. of Math. Anhui Normal University Wuhu 241000 Anhui Dept. of Math. Huzhou Teachers College Huzhou 313000 Zhejiang Dept. of Math. Shanghai Jiaotong University Shanghai 200240 Dept. of Applied Math. Donghua University Shanghai 200051 division of computational science E-Institutes of Shanghai Universities at SJTU Shanghai 200240

In this paper, the heat conductive problem with boundary perturbations lS considered. Using the solvability of the problem, two eigenfunctions corresponding to two eigenvalues for the nm-th modular form are obtained.

关键词： perturbation heat conduction solvability

Singular perturbation for the weakly nonlinear reaction diffusion equation with boundary perturbation

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Applied mathematics and Mechanics(English Edition) 2008年第8期29卷 1105-1110页

作者： mo Jia-qi department of mathematics Anhui Normal University Wuhu 241000 Anhui Province P. R. China department of mathematics Huzhou Teachers College Huzhou 313000 Zhejiang Province P. R. China division of computational science E-Institutes of Shanghai Universities at Shanghai Jiaotong University Shanghai 200240 P. R. China

In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.

关键词： nonlinear reaction diffusion singular perturbation boundary perturbation