Asymptotic behavior of the unbounded solutions to some degenerate boundary layer equations revisited期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Asymptotic behavior of the unbounded solutions to some degenerate boundary layer equations revisited

Authors:

Institution:

(1) LAMFA, CNRS UMR 6140, Faculté de Mathématiques et d’Informatique, Université de Picardie Jules Verne, 33 rue Saint-Leu, FR-80039 Amiens, France;(2) Department of Mathematics, University of Pécs, PMMF, Boszorkany u. 2, H-7624 Pécs, Hungary

Abstract:

We reconsider the boundary-layer flow of a non-Newtonian fluid corresponding to the classical Ostwald de Waele power-law model. The physical problem can be described in terms of solutions of the degenerate differential equation

$(|f^{\prime\prime}|^{n-1}f^{\prime\prime})^{\prime} + ff^{\prime\prime} - \beta f^{\prime2} = 0,$

posed on the interval (0, ∞), in which β < 0 and the real number (the power law index) n ≥ 1. This paper deals with the asymptotic behavior of any global unbounded solution; that is a solution satisfying

${\mathop{{\rm lim}}\limits_{\eta\rightarrow\infty}}|f(\eta)| = \infty$

. Received: 8 March 2006 Revised: 8 January 2007

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 34B15 34B60 76D10

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