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《Journal of Anhui Normal University(Natural Science)》 2013-01
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The Asymptotic Solution of a Class of Nonlinear Singularly Perturbed Problems

FANG Jing,OUYANG Cheng(Department of Mathematics,Huzhou Teachers College,Zhejiang 313000,China)  
Using the matching asymptotic expansion method,a class of nonlinear singularly perturbed boundary value problems on an infinite long region is studied,and the uniformly valid asymptotic expansion with the first order for the solution is given.First solving the outer expansion,and then solving interior expansion with the contraction transformation.Using the generalized integral and Taylor expansion,the internal expansion and the outer one are matched,and the uniformly valid compound expansion is obtained.Through studying this class of new nonlinear problems on the infinite long region,the studied range of the similar problems is expanded.And it is provided with a reference for the research on the related singularly perturbed problems.
【Fund】: 国家自然科学基金(11071205 10902076);; 浙江省自然科学基金(Y6110502);; 浙江省精品课程《常微分方程》
【CateGory Index】: O175.8
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【Citations】
Chinese Journal Full-text Database 5 Hits
1 HAN Xiang-lin (Department of Mathematics, Huzhou Teachers' College, Huzhou 313000, China);THE PERTURBED PROBLEM OF NONLINEAR EQUATION[J];Journal of Anhui Normal University(Natural Science);2001-04
2 HAN Xiang lin (Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China);THE PRRTURBED SOLUTION OF NONLINEAR EQUATION WITH AN UNBOUNDED INTERVAL[J];Journal of Anhui Normal University(Natural Science);2003-01
3 YAO Jing-sun(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China);Asymptotic Solution to a Nonlinear Singularly Perturbed Problem[J];Journal of Anhui Normal University(Natural Science);2006-02
4 LI Huang,OUYANG Cheng,HAN Xiang-lin(Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China);Asymptotic Solution to the Perturbation Problem of Nonlinear Equation with an Unbounded Interval[J];Journal of Anhui Normal University(Natural Science);2010-01
5 LI Huang(School of Science,Hangzhou Dianzi University of Technology,Hangzhou 310018,China);A Singular Perturbation Boundary Value Problem with Unbounded Interval[J];Journal of Huzhou Teachers College;2011-01
【Co-citations】
Chinese Journal Full-text Database 5 Hits
1 GAO Fa-bao,LU Shi-ping(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China);Global Stability for a Class of Third Order Nonlinear Systems with Three Nonlinear Terms[J];Journal of Anhui Normal University(Natural Science);2008-03
2 LI Huang,OUYANG Cheng,HAN Xiang-lin(Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China);Asymptotic Solution to the Perturbation Problem of Nonlinear Equation with an Unbounded Interval[J];Journal of Anhui Normal University(Natural Science);2010-01
3 LI Qing,YAO Jing-sun(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241003,China);Singularly Perturbed Problem for the Second-Order Nonlinear Equation with a Locally Strongly Stable Reduce Solution[J];Journal of Anhui Normal University(Natural Science);2012-06
4 CHEN Sheng,TANG Rong-rong(College of Science,Huzhou Teachers College,Huzhou 313000,China);Asymptotic Solution for a Class of the Perturbation Equation with an Unbounded Interval[J];Journal of Hangzhou Normal University(Natural Science Edition);2011-01
5 LI Huang(School of Science,Hangzhou Dianzi University of Technology,Hangzhou 310018,China);A Singular Perturbation Boundary Value Problem with Unbounded Interval[J];Journal of Huzhou Teachers College;2011-01
【Secondary Citations】
Chinese Journal Full-text Database 10 Hits
1 HAN Xiang-lin (Department of Mathematics, Huzhou Teachers' College, Huzhou 313000, China);THE PERTURBED PROBLEM OF NONLINEAR EQUATION[J];Journal of Anhui Normal University(Natural Science);2001-04
2 HAN Xiang lin (Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China);THE PRRTURBED SOLUTION OF NONLINEAR EQUATION WITH AN UNBOUNDED INTERVAL[J];Journal of Anhui Normal University(Natural Science);2003-01
3 YAO Jing-sun(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China);Asymptotic Solution to a Nonlinear Singularly Perturbed Problem[J];Journal of Anhui Normal University(Natural Science);2006-02
4 LI Huang,OUYANG Cheng,HAN Xiang-lin(Department of Mathematics,Huzhou Teachers College,Huzhou 313000,China);Asymptotic Solution to the Perturbation Problem of Nonlinear Equation with an Unbounded Interval[J];Journal of Anhui Normal University(Natural Science);2010-01
5 WU Qin-kuan Dept of Basic Course, Nanjing Institute of Technology, Nanjing 210013;The Shift of Shock Position for a Class of Sensitive Boundary Value Problems[J];Chinese Journal of Engineering Mathematics;2004-04
6 WANG Li-jie(Faculty of Science, Huzhou Teachers College, Huzhou313000,China);The Matching Solving Method for a Class of Nonlinear Singularly Perturbed Problems[J];College Mathematies;2005-04
7 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
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9 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
10 Tang Rongrong (Department of Mathematics,Huzhou Teachers College,Huzhou 313000;Division of Computational Science,E-Institute of Shanghai Universities,at SJTU,Shanghai 200240);On a Class of Singularly Perturbed Problems with Boundary Perturbation[J];Acta Mathematica Scientia;2008-03
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