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.
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Aïboudi, M., Brighi, B. On the solutions of a boundary value problem arising in free convection with prescribed heat flux. Arch. Math. 93, 165–174 (2009). https://doi.org/10.1007/s00013-009-0023-6
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DOI: https://doi.org/10.1007/s00013-009-0023-6