Sur un problème aux limites associé à l'équation différentielle f'''+ff''+2f'^2=0

Bernard Brighi (1)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]

We are interested by the differential equation $f'''+ff''+2f'^2=0$, arising in fluid mechanics and in magnetohydrodynamics. This differential equation, that is a particular case of a more general one, has a first integral which allows to obtain several results by elementary means, and explicit constants. In addition, for given $a,b\in\R$, we will study the solutions of the above differential equation, satisfying the boundary conditions $f(0)=a$, $f'(0)=b\geq 0$ and $f'(t)\to 0$ as $t\to+\infty$.

Domaines: Systèmes dynamiques [math.DS]

Bernard Brighi. Sur un problème aux limites associé à l'équation différentielle f'''+ff''+2f'^2=0. 2008. ⟨hal-00347191⟩