Abstract
The purpose of this paper is to study the autonomous third order non linear differential equation f’’’ + ff’’ + g(f’) = 0 on [0, +∞[ with g(x) = βx(x − 1) and β > 1, subject to the boundary conditions f(0) = a ∈ R, f’(0) = b < 0 and f’(t) → λ ∈ {0, 1} as t → +∞. This problem arises when looking for similarity solutions to problems of boundary-layer theory in some contexts of fluids mechanics, as mixed convection in porous medium or flow adjacent to a stretching wall. Our goal, here is to investigate by a direct approach this boundary value problem as completely as possible, say study existence or non-existence and uniqueness solutions and the sign of this solutions according to the value of the real parameter β.
Highlights
The purpose of this paper is to study the autonomous third order non linear differential equation f + f f + g(f ) = 0 on [0, +∞[ with g(x) = βx(x − 1) and β > 1, subject to the boundary conditions f (0) = a ∈ R, f (0) = b < 0 and f (t) → λ ∈ {0, 1} as t → +∞
Here is to investigate by a direct approach this boundary value problem as completely as possible, say study existence or non-existence and uniqueness solutions and the sign of this solutions according to the value of the real parameter β
In fluid mechanics, the problems are usually governed by systems of partial differential equations
Summary
The problems are usually governed by systems of partial differential equations. Assume that fc is convex on its right maximal interval of existence [0, Tc) and fc(t) → +∞ as t → Tc. There exist t0 ∈ [0, T0) , which the function H2 is decreasing for t > t0, this is a contradiction as t →Tc. Proposition 4.2.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
