On the Solutions of Falkner-Skan Equation

Résumé

We consider the differential equation f''' +ff'' +β(f'^2 - 1) = 0, with β > 0. In order to prove the existence of solutions satisfying the boundary conditions f (0) = a ≥ 0, f'(0) = b ≥ 0 and f'(+∞) = -1 or 1 for 0 < β ≤ 1/2 . We use shooting technique and consider the initial conditions f (0) = a, f'(0) = b and f”˜'(0) = c. We prove that there exists an infinitely many solutions such that f'(+∞) = 1.

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