publication . Article . 2009

On the structure of similarity solutions of a differential equation arising from boundary layer problem

Hung, Shih-Hsun; Wang, Ching-An;
Open Access
  • Published: 01 Nov 2009 Journal: Journal of Mathematical Analysis and Applications, volume 359, issue 1, pages 333-351 (issn: 0022-247X, Copyright policy)
  • Publisher: Elsevier BV
Abstract We consider an ordinary differential equation f ‴ − f f ″ − β f ′ 2 = 0 with f ( 0 ) = a , f ′ ( 0 ) = 1 , f ′ ( ∞ ) : = lim t → ∞ f ′ ( t ) = 0 , where β is a real constant. The given problem may arise from the study of steady free convection flow over a vertical semi-infinite flat plate in a porous medium, or the study of a boundary layer flow over a vertical stretching wall. In this paper, the structure of solutions for the cases of β ⩾ − 2 is studied. Combining the results of [B. Brighi, T. Sari, Blowing-up coordinates for a similarity boundary layer equation, Discrete Contin. Dyn. Syst. 5 (2005) 929–948; J.-S. Guo, J.-C. Tsai, The structure of solu...
free text keywords: Applied Mathematics, Analysis, Boundary layer problem, Similarity solutions, Blow-up coordinate, Phase portrait analysis, Free convection flow, Boundary layer, Differential equation, Third order differential equation, Similarity solution, Porous medium, Shooting method, Mathematical analysis, Ordinary differential equation, Mathematics
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