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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (3) :485-494    DOI: 10.1007/s10255-012-0164-4
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Singularly Perturbed Boundary Value Problems for a Class of Second Order Turning Point on Infinite Interval
Hai-bo LU, Ming-kang NI, Li-mengWU
1. Department of Mathematics, East China Normal University, Shanghai 200062, China;
2. State Key Laboratory of Brain and Cognitive Sciences, 15, Datun Road, Chaoyang District, Beijing
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Abstract This article solved the asymptotic solution of a singularly perturbed boundary value problem with second order turning point, encountered in the dissipative equilibrium vector field of the coupled convection disturbance kinetic equations under the constrained filed and the gravity. Using the matching of asymptotic expansions, the formal asymptotic solution is constructed. By using the theory of differential inequality the uniform validity of the asymptotic expansion for the solution is proved.
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Keywordssingular perturbation   asymptotic expansion   turning point   infinite interval     
Abstract: This article solved the asymptotic solution of a singularly perturbed boundary value problem with second order turning point, encountered in the dissipative equilibrium vector field of the coupled convection disturbance kinetic equations under the constrained filed and the gravity. Using the matching of asymptotic expansions, the formal asymptotic solution is constructed. By using the theory of differential inequality the uniform validity of the asymptotic expansion for the solution is proved.
Keywordssingular perturbation,   asymptotic expansion,   turning point,   infinite interval     
Received: 2010-10-18;
Fund:Supported by the National Natural Science Foundation of China (No. 11071075, 11171113), the NNFC-the Knowledge Innovation Program of Chinese Academy of Science (No. 30921064, 90820307), and E-Institutes of Shanghai Municipal Education Commission (No. E03004).
Cite this article:   
.Singularly Perturbed Boundary Value Problems for a Class of Second Order Turning Point on Infinite Interval[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(3): 485-494
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http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0164-4      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I3/485
 
[1] Hou, L., Cai, L. Computationla Study On the Non-Newtonian Boundary-layer Impact Problem. Journal of ECNU, 5: 2-10 (2008) (in Chinese)
[2] Hou, L. Asymptotic Solutions of the Nonlinear Eigenvalue Problems in the Multi-field Coupled Dynamic Equations. Journal of ECNU, 5: 99-112 (2010)
[3] O’Malley, R.E., JR. Singularly Perturbed Linear Two-Point Boundary Value Problems. SIAM Review, 50: 459-482 (2008)
[4] Ni, M.K., Lin, W.Z. Asymptotic Theory of Singular Perturbation. Higher Education Press, Beijing, 2009 (in Chinese)
[5] Cheng, H. Advanced Analytic Methods in Applied Mathematics, Science, and Engineering. LuBan Press, Boston, 2007
[6] Fenichel, N. Geometric Singular Perturbation Theory for Ordinary Differential Equations. J. Diff. Equ., 31: 53-98 (1979)
[7] Wasow, W. Linear Turning Point Theory. Springer-Verlag, Berlin and New York, 1985
[8] Wong, R., Yang, H. On a Boundary-Layer Problem. Stud. Appl. Math., 108: 369-398 (2002)
[9] Wong, R., Yang, H. On an Internal Boundary Layer Problem. J. Comp. Appl. Math., 144: 301-323 (2002)
[10] Wong, R., Yang, H. On the Ackerberg-O’Malley Resonance. Stud. Appl. Math., 110: 157-179 (2003)
[11] Il’in, A.M. Matching of Asymptotic Expansions of Solutions of Boundary Value Prolems. AMS, 1991
[12] Dolbeeva, S.F., Chizh, E.A. Asymptotics of a second-order differential equation with a small parameter in the case when the reduced equation has two solutions. Computational Mathematics and Mathematical Physics, 48(1): 30-42 (2008)
[13] De Masschalck, P. Ackerberg-O’Malley Resonance in Boundary Value Problens with a Turning Point of Any Order. Commun. Pure. Appl. Anal., 6: 311-333 (2007)
[14] Wang, Z.X. Introduction to Special Function (in Chinese). Peking University Press, Beijing, 2000, 288-310
[15] Nagumo, M. Uber die Differentialgleichung y″ = f(x, y, y′). Proc. Phys. Math. Soc. Japan, 19: 861-866 (1937)
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