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Archiv der Mathematik

, Volume 93, Issue 2, pp 165–174 | Cite as

On the solutions of a boundary value problem arising in free convection with prescribed heat flux

  • Mohamed Aïboudi
  • Bernard Brighi
Article

Abstract

For given \({a \in \mathbb {R}}\) , c < 0, we are concerned with the solution f b of the differential equation f ′′′ + ff ′′ + g(f ′) = 0 satisfying the initial conditions f(0) = a, f ′ (0) = b, f ′′ (0) = c, where g is some nonnegative subquadratic locally Lipschitz function. It is proven that there exists b * > 0 such that f b exists on [0, + ∞) and is such that \({f'_b(t) \to 0}\) as t → + ∞, if and only if b ≥ b *. This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising in fluid mechanics, and especially in boundary layer theory.

Mathematics Subject Classification (2000)

34B15 34C11 76D10 

Keywords

Boundary layer Similarity solution Third order nonlinear differential equation Boundary value problem Fluid mechanics 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité d’Oran (Es-Senia)OranAlgeria
  2. 2.Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et ApplicationsMulhouse CedexFrance

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