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

2007/07/11 by Mohamed Aïboudi, Aïboudi, Mohamed, Bernard Brighi +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.0707.1628

arxiv created 2007/07/11 · arxiv updated 2009/12/01

Abstract

For given a∈\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< 0, 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)→ 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.

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