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《Journal of Anhui Normal University(Natural Science)》 2009-04
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The Overlapping Layer Solution to Nonlinear Singularly Perturbed Boundary Value Problem

GE Zhi-xin(College of Mathematics and Computer Science,Anhui Normal University, Wuhu 241000,China)  
A singularly perturbed problem of the nonlinear equation is considered.Under suitable conditions,using the stretched variables,the formal asymptotic expansion with the overlapping layer of a solution is provided.And using the theory of differential inequalities,the uniformly valid behavior of its expansion is proved.The method and the result are meaningful for the study of nonlinear isngularly perturbed boundary value problems.
【Fund】: 教育部自然科学基金重大项目(207047);; 安徽省自然科学基金(2005kj031ZD 050460103)
【CateGory Index】: O175.8
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【Citations】
Chinese Journal Full-text Database 5 Hits
1 Liu Shude(Anhui Normal University,Wuhu 241000);NONMONOTONE INTERIOR LAYER BEHAVIOR FOR SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS WITH TURNING POINTS[J];APPLIED MATHEMATICS A JOURNAL OF CHINESE UNIVERSITIES;1994-02
2 ZHANG Han-lin, MO Jia-qi (College of Applied Science, Beijing University of Technology, Beijing 100022, China; Department of Mathematics, Anhui Normal University, Wuhu 241000,China);The Overlaping Layer Solution to Nonlinear Singularly Perturbed Boundary Value Problem[J];Journal of Beijing University of Technology;2007-01
3 TANG Rong-rong (Dept. of Math., Huzhou Teachers College,Huzhou 313000, China);A CLASS OF SINGULARLY PERTURBED PROBLEMS OF NONLINEAR SYSTEM[J];Journal of Mathematics;2004-03
4 Ouyang Cheng (Department of Mathematics, Huzhou Teachers College, Huzhou 313000);A Singular Perturbation to Robin Boundary Value Problem of Semi-linear ODF of Second Order[J];Acta Mathematiea Scientia;2005-02
5 FENG Mao-chun(Huzhou Teachers College,Huzhou 313000,China);The Estimation of Singularly Perturbed Group of Second Degree Robin Problems[J];Mathematica Applicata;2007-03
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 TANG Rong-rong(Faculty of Sciences,Huzhou Teachers College,Huzhou 313000,China;Division of Computational Science,E-Institue of Shanghai Universities,at SJTU,Shanghai 200240,China);Asympotic solution and solvable conditions for a class of nonlinear problem with boundary perturbation[J];Applied Mathematics A Journal of Chinese Universities(Ser.A);2007-02
2 CHEN Xiu (Hefei United University, Hefei230022);Singular Perturbation of Robin Boundary Value Problems for Second Order Nonlinear Systems with Turning Points[J];JOURNAL OF MATHEMATICS FOR TECHNOLOGY;2000-02
3 GE Zhi-xin,MO Jia-qi,LIU Shu-de(Department of Mathematics,Anhui Normal University,Wuhu 241000,China);Quadratic Singularly Perturbed Problem with Nonlinear Boundary Conditions[J];Journal of Anqing Teachers College(Natural Science Edition);2008-03
4 GE Zhi-xin,GAO Xiao-hong,LIU Shu-de(Dept.of Math.,Anhui Normal University,Wuhu 241000,China);Homotopic Mapping Solving Method for a Class of Dynamic Model of Infectious Diseases[J];Journal of Anqing Teachers College(Natural Science Edition);2009-01
5 CHEN Xiu(Department of Mathematics and Physics,Hefei University,Hefei 230022,China);Different Layers Behaviour in Singularly Perturbed Robin Boundary Value Problem of Nonlinear Systems[J];Journal of Hefei University(Natural Sciences);2006-01
6 MO Jia-qi~(1,2),HE Ming~(2,3),XIE Feng~(2,4)(1.Department of Mathematics,Anhui Normal University,Wuhu 241000,Anhui Province,China;2.Division of Computational Science,E-Institute of Shanghai Universities,at SJTU,Shanghai 200240,China;3.Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China;4.Department of Applied Mathematics,Donghua University,Shanghai 201620, China);Asymptotic Analysis of Epidemical Dynamic Ecotogical Model[J];Journal of Jilin University(Science Edition);2006-06
7 TANG Rong-rong (Department of Mathematics, Huzhou Teachers College, Huzhou 313000, Zhejiang, China);The shock solutions for a class of nonlinear problems[J];Journal of Lanzhou University(Natural Sciences);2006-03
8 OUYANG Cheng(Department of Mathematics,Huzhou University,Huzhou 313000,Zhejiang Province,China);Asymptotic Solution of Initial Value Problems for Differential-difference Equation with Small Time Delay[J];Journal of Jilin University(Science Edition);2008-04
9 TANG Rong-rong(Faculty of Science,Huzhou Teachers' College,Huzhou 313000,China);Approximate Solving Methods For Two Nonlinean Wave Equations[J];Journal of Nanchang University(Natural Science);2006-01
10 OUYANG Cheng~(1,2) (1.Department of Mathematics,Huzhou Teachers College,Huzhou 313000,Zhejiang,China; 2.Division of Computational Science,E-Institutes of Shanghai Universities at SJTU,Shanghai 200240,China);Shock solution to nonlinear singularly perturbed equation of second-order[J];Journal of Lanzhou University(Natural Sciences);2009-01
【Secondary Citations】
Chinese Journal Full-text Database 3 Hits
1 FENG Mao-chun (Huzhou Teachers College,Huzhou313000,China);The estimation of solution for singularly perturbed problems of second degree equation via differential inequality[J];Pure and Applied Mathematics;2004-02
2 OUYANG Cheng MO Jia-qi (Huzhou Teachers College, Huzhou Zhejiang 313000 China);The Nonlinear Singularly Perturbed Problems for Predator-Prey Reaction Diffusion Equations[J];Journal of Biomathematics;2005-02
3 OU Yang cheng 1,MO Jia qi 2 (1. Dept. of Math., Huzhou Teachers College, Zhejiang Huzhou 313000,China;2. Dept. of Math., Anhui Normal University, AnHui Wuhu 241000,China);A Nonlinear Equation for Turning Point Problem[J];Mathematica Applicata;2001-02
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