The velocity and shear stress functions of the Falkner-Skan equation arising in boundary layer theory

Journal of Mathematical Analysis and Applications

Volumn 328, Issue 2, 2007, Pages 1297-1308

  Yang, G C ^a   Lan, K Q ^b  

^a CHENGDU UNIVERSITY OF INFORMATION TECHNOLOGY   (China)

^b RYERSON UNIVERSITY   (Canada)

Author keywords

Boundary layer problem; Compactness; Falkner Skan equation; Shear stress function; Singular integral equation; Velocity function

Indexed keywords

EID: 33845888812     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.06.042     Document Type: Article

References (21)

1. Agarwal R.P., and O'Regan D. Singular integral equations arising in Homann flow. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 9 4 (2002) 481-488
2. Acheson D.J. Elementary Fluid Dynamics (1990), Oxford Univ. Press, New York
3. Brown S.N., and Stewartson K. On the reversed flow solutions of the Falkner-Skan equations. Mathematika 13 25 (1996) 1-6
4. Coppel W.A. On a differential equation of boundary-layer theory. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 253 1023 (1960) 101-136
5. Craven A.H., and Peletier L.A. On the uniqueness of solutions of the Falkner-Skan equation. Mathematika 19 (1972) 129-133
6. Hartman P. Ordinary Differential Equations. Class. Appl. Math. vol. 38 (2002), SIAM, Philadelphia, PA
7. Hartman P. On the existence of similar solutions of some boundary layer problems. SIAM J. Math. Anal. 3 1 (1972) 120-147
8. Hastings S.P. An existence theorem for a class of nonlinear boundary value problems including that of Falkner and Skan. J. Differential Equations 9 (1971) 580-590
9. Hastings S.P. Reversed flow solutions of the Falkner-Skan equations. SIAM J. Appl. Math. 22 2 (1972) 329-334
10. K.Q. Lan, G.C. Yang, Positive solutions of the Falkner-Skan equation arising in the boundary layer theory, Canad. Math. Bull., in press
11. Libby P.A., and Liu T.M. Further solutions of the Falkner-Skan equation. AIAA J. 5 5 (1967) 1040-1042
12. Na T.Y. Computational Methods in Engineering Boundary Value Problems (1979), Academic Press
13. Riley N., and Weidman P.D. Multiple solutions of the Falkner-Skan equation for flow past a stretching boundary. SIAM J. Appl. Math. 49 5 (1989) 1350-1358
14. Schlichting H., and Gersten K. Boundary-Layer Theory. eighth ed. (2000), Springer, Berlin
15. Schrader K. A generalization of the Helly selection theorem. Bull. Amer. Math. Soc. 78 3 (1972) 415-419
16. Tam K.K. A note on the existence of a solution of the Falkner-Skan equation. Canad. Math. Bull. 13 (1970) 125-127
17. Wang J., Gao W., and Zhang Z. Singular nonlinear boundary value problems arising in boundary layer theory. J. Math. Anal. Appl. 233 (1999) 246-256
18. Weyl H. On the differential equations of the simplest boundary-layer problems. Ann. of Math. 43 2 (1942) 381-407
19. Yang G.C. Existence of solutions to the third-order nonlinear differential equations arising in boundary layer theory. Appl. Math. Lett. 16 (2003) 827-832
20. ′ 2) = 0 with λ ∈ (- frac(1, 2), 0) arising in boundary layer theory. Appl. Math. Lett. 17 (2004) 1261-1265
21. ′ 2) = 0 arising in boundary layer theory. Nonlinear Funct. Anal. Appl. 10 (2005) 117-122