메뉴 건너뛰기




Volumn 199, Issue 2, 2004, Pages 290-325

A geometric analysis of the Lagerstrom model problem

Author keywords

Blow up; Invariant manifolds; Singular perturbations

Indexed keywords


EID: 1942478419     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2003.08.004     Document Type: Article
Times cited : (22)

References (35)
  • 2
    • 0012494568 scopus 로고
    • Gronwall inequalities
    • Carleton University, Ottawa
    • P.R. Beesack, Gronwall inequalities, in: Carleton Mathematical Lecture Notes, Vol. 11, Carleton University, Ottawa, 1975.
    • (1975) Carleton Mathematical Lecture Notes , vol.11
    • Beesack, P.R.1
  • 3
    • 21344442343 scopus 로고    scopus 로고
    • Partially hyperbolic fixed points with constraints
    • P. Bonckaert, Partially hyperbolic fixed points with constraints, Trans. Amer. Math. Soc. 348 (3) (1996) 997-1011.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , Issue.3 , pp. 997-1011
    • Bonckaert, P.1
  • 4
    • 0015025343 scopus 로고
    • On the Lagerstrom mathematical model for viscous flow at low Reynolds number
    • W.B. Bush, On the Lagerstrom mathematical model for viscous flow at low Reynolds number, SIAM J. Appl. Math. 20 (2) (1971) 279-287.
    • (1971) SIAM J. Appl. Math. , vol.20 , Issue.2 , pp. 279-287
    • Bush, W.B.1
  • 5
    • 0017905402 scopus 로고
    • Proof of some asymptotic results for a model equation for low Reynolds number flow
    • D.S. Cohen, A. Fokas, P.A. Lagerstrom, Proof of some asymptotic results for a model equation for low Reynolds number flow, SIAM J. Appl. Math. 35 (1) (1978) 187-207.
    • (1978) SIAM J. Appl. Math. , vol.35 , Issue.1 , pp. 187-207
    • Cohen, D.S.1    Fokas, A.2    Lagerstrom, P.A.3
  • 8
    • 0002252484 scopus 로고
    • A method of desingularization for analytic two-dimensional vector field families
    • Z. Denkowska, R. Roussarie, A method of desingularization for analytic two-dimensional vector field families, Bol. Soc. Brasil Mat. 22 (1) (1991) 93-126.
    • (1991) Bol. Soc. Brasil Mat. , vol.22 , Issue.1 , pp. 93-126
    • Denkowska, Z.1    Roussarie, R.2
  • 9
    • 0002336002 scopus 로고
    • Techniques in the theory of local bifurcations: Blow-up, normal forms, nilpotent bifurcations, singular perturbations
    • D. Schlomiuk (Ed.), Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series C, Kluwer Academic Publishers, Dordrecht
    • F. Dumortier, Techniques in the theory of local bifurcations: blow-up, normal forms, nilpotent bifurcations, singular perturbations, in: D. Schlomiuk (Ed.), Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Series C, Mathematical and Physical Sciences, Vol. 408, Kluwer Academic Publishers, Dordrecht, 1993.
    • (1993) Mathematical and Physical Sciences , vol.408
    • Dumortier, F.1
  • 11
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations 31 (1979) 53-98.
    • (1979) J. Differential Equations , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 12
    • 84968514940 scopus 로고
    • A note on a functional inequality
    • H.E. Gollwitzer, A note on a functional inequality, Proc. Amer. Math. Soc. 23 (1969) 642-647.
    • (1969) Proc. Amer. Math. Soc. , vol.23 , pp. 642-647
    • Gollwitzer, H.E.1
  • 13
    • 0003285244 scopus 로고
    • Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
    • Springer, New York
    • J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, in: Applied Mathematical Sciences, Vol. 42, Springer, New York, 1983.
    • (1983) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 14
    • 0008038389 scopus 로고
    • Singular perturbations for a nonlinear differential equation with a small parameter
    • G.C. Hsiao, Singular perturbations for a nonlinear differential equation with a small parameter, SIAM J. Math. Anal. 4 (1973) 283-301.
    • (1973) SIAM J. Math. Anal. , vol.4 , pp. 283-301
    • Hsiao, G.C.1
  • 15
    • 0025387093 scopus 로고
    • On Lagerstrom's model of slow incompressible viscous flow
    • C. Hunter, M. Tajdari, S.D. Boyer, On Lagerstrom's model of slow incompressible viscous flow, SIAM J. Appl. Math. 50 (1) (1990) 48-63.
    • (1990) SIAM J. Appl. Math. , vol.50 , Issue.1 , pp. 48-63
    • Hunter, C.1    Tajdari, M.2    Boyer, S.D.3
  • 16
    • 0002316532 scopus 로고
    • Geometric Singular Perturbation Theory
    • Dynamical Systems, Springer, New York
    • C.K.R.T. Jones, Geometric Singular Perturbation Theory, in: Dynamical Systems, Springer Lecture Notes in Mathematics, Vol. 1609, Springer, New York, 1995.
    • (1995) Springer Lecture Notes in Mathematics , vol.1609
    • Jones, C.K.R.T.1
  • 17
    • 0001369397 scopus 로고
    • Low Reynolds number flow past a circular cylinder
    • S. Kaplun, Low Reynolds number flow past a circular cylinder, J. Math. Mech. 6 (1957) 595-603.
    • (1957) J. Math. Mech. , vol.6 , pp. 595-603
    • Kaplun, S.1
  • 18
    • 0001552939 scopus 로고
    • Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers
    • S. Kaplun, P.A. Lagerstrom, Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers, J. Math. Mech. 6 (1957) 585-593.
    • (1957) J. Math. Mech. , vol.6 , pp. 585-593
    • Kaplun, S.1    Lagerstrom, P.A.2
  • 19
    • 0030088284 scopus 로고    scopus 로고
    • Asymptotics beyond all orders for a low Reynolds number flow
    • J.B. Keller, M.J. Ward, Asymptotics beyond all orders for a low Reynolds number flow, J. Eng. Math. 30 (1-2) (1996) 253-265.
    • (1996) J. Eng. Math. , vol.30 , Issue.1-2 , pp. 253-265
    • Keller, J.B.1    Ward, M.J.2
  • 20
    • 0036052772 scopus 로고    scopus 로고
    • Extending geometric singular perturbation theory to non-hyperbolic points - Fold and canard points in two dimensions
    • M. Krupa, P. Szmolyan, Extending geometric singular perturbation theory to non-hyperbolic points - fold and canard points in two dimensions, SIAM J. Math. Anal. 33 (2) (2001) 286-314.
    • (2001) SIAM J. Math. Anal. , vol.33 , Issue.2 , pp. 286-314
    • Krupa, M.1    Szmolyan, P.2
  • 21
    • 0029514864 scopus 로고
    • A hybrid asymptotic-numerical method for low Reynolds number flow past a cylindrical body
    • M.C.A. Kropinski, M.J. Ward, J.B. Keller, A hybrid asymptotic-numerical method for low Reynolds number flow past a cylindrical body, SIAM J. Appl. Math. 55 (6) (1995) 1484-1510.
    • (1995) SIAM J. Appl. Math. , vol.55 , Issue.6 , pp. 1484-1510
    • Kropinski, M.C.A.1    Ward, M.J.2    Keller, J.B.3
  • 22
    • 1942531437 scopus 로고
    • A course on perturbation methods
    • Lecture Notes by M. Mortell, National University of Ireland, Cork
    • P.A. Lagerstrom, A course on perturbation methods, Lecture Notes by M. Mortell, National University of Ireland, Cork, 1966.
    • (1966)
    • Lagerstrom, P.A.1
  • 23
    • 0003272695 scopus 로고
    • Matched Asymptotic Expansions: Ideas and Techniques
    • Springer, New York
    • P.A. Lagerstrom, Matched Asymptotic Expansions: Ideas and Techniques, in: Applied Mathematical Sciences, Vol. 76, Springer, New York, 1988.
    • (1988) Applied Mathematical Sciences , vol.76
    • Lagerstrom, P.A.1
  • 24
    • 0015286459 scopus 로고
    • Basic concepts underlying singular perturbation techniques
    • P.A. Lagerstrom, R.G. Casten, Basic concepts underlying singular perturbation techniques, SIAM Rev. 14 (1) (1972) 63-120.
    • (1972) SIAM Rev. , vol.14 , Issue.1 , pp. 63-120
    • Lagerstrom, P.A.1    Casten, R.G.2
  • 25
    • 0021451379 scopus 로고
    • Note on logarithmic switchback terms in regular and singular perturbation expansions
    • P.A. Lagerstrom, D.A. Reinelt, Note on logarithmic switchback terms in regular and singular perturbation expansions, SIAM J. Appl. Math. 44 (3) (1984) 451-462.
    • (1984) SIAM J. Appl. Math. , vol.44 , Issue.3 , pp. 451-462
    • Lagerstrom, P.A.1    Reinelt, D.A.2
  • 26
    • 0002790544 scopus 로고
    • Über die Stokes'sche Formel, und über eine verwandte Aufgabe in der Hydrodynamik
    • C.W. Oseen, Über die Stokes'sche Formel, und über eine verwandte Aufgabe in der Hydrodynamik, Ark. Math. Astronom. Fys. 6 (29) (1910).
    • (1910) Ark. Math. Astronom. Fys. , vol.6 , Issue.29
    • Oseen, C.W.1
  • 27
    • 85030877040 scopus 로고    scopus 로고
    • Rigorous asymptotic expansions for Lagerstrom's model equation - A geometric approach
    • in preparation
    • N. Popović, P. Szmolyan, Rigorous asymptotic expansions for Lagerstrom's model equation - a geometric approach, in preparation.
    • Popović, N.1    Szmolyan, P.2
  • 28
    • 84958437158 scopus 로고
    • Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder
    • I. Proudman, J.R.A. Pearson, Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech. 2 (1957) 237-262.
    • (1957) J. Fluid Mech. , vol.2 , pp. 237-262
    • Proudman, I.1    Pearson, J.R.A.2
  • 29
    • 0016534495 scopus 로고
    • On the asymptotic solution of the Lagerstrom model equation
    • S. Rosenblat, J. Shepherd, On the asymptotic solution of the Lagerstrom model equation, SIAM J. Appl. Math. 29 (1) (1975) 110-120.
    • (1975) SIAM J. Appl. Math. , vol.29 , Issue.1 , pp. 110-120
    • Rosenblat, S.1    Shepherd, J.2
  • 30
    • 1942435379 scopus 로고
    • Note on the Lagerstrom singular perturbation models
    • L.A. Skinner, Note on the Lagerstrom singular perturbation models, SIAM J. Appl. Math. 41 (2) (1981) 362-364.
    • (1981) SIAM J. Appl. Math. , vol.41 , Issue.2 , pp. 362-364
    • Skinner, L.A.1
  • 31
    • 0000542238 scopus 로고
    • On the structure of local homeomorphisms of Euclidean n-space, II
    • S. Sternberg, On the structure of local homeomorphisms of Euclidean n-space, II, Amer. J. Math. 80 (1958) 623-631.
    • (1958) Amer. J. Math. , vol.80 , pp. 623-631
    • Sternberg, S.1
  • 32
    • 0001041112 scopus 로고
    • On the effect of the internal friction of fluids on the motion of pendulums
    • G.G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums, Trans. Camb. Philos. Soc. 9 (Part II) (1851) 8-106.
    • (1851) Trans. Camb. Philos. Soc. , vol.9 , Issue.PART II , pp. 8-106
    • Stokes, G.G.1
  • 33
    • 0000152319 scopus 로고
    • Partially hyperbolic fixed points
    • F. Takens, Partially hyperbolic fixed points, Topology 10 (1971) 133-147.
    • (1971) Topology , vol.10 , pp. 133-147
    • Takens, F.1
  • 34
    • 5744229125 scopus 로고    scopus 로고
    • Asymptotic expansions using blow-up
    • ZAMP, to appear
    • S. van Gils, M. Krupa, P. Szmolyan, Asymptotic expansions using blow-up, ZAMP, to appear.
    • van Gils, S.1    Krupa, M.2    Szmolyan, P.3
  • 35
    • 0000274860 scopus 로고
    • Second approximations to viscous fluid motion
    • A.N. Whitehead, Second approximations to viscous fluid motion, Quart. J. Math. 23 (1889) 143-152.
    • (1889) Quart. J. Math. , vol.23 , pp. 143-152
    • Whitehead, A.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.