21810 articles – 15605 references  [version française]
 HAL: hal-00020172, version 1
 arXiv: math/0603080
 Mathematical Methods in the Applied Sciences vol. 28, 4 (2005) pp. 479-503
 On similarity solutions for boundary layer flows with prescribed heat flux
 B. Brighi 1, J. -D. Hoernel 2
 (2004)
 This paper is concerned with existence, uniqueness and behavior of the solutions of the autonomous third order nonlinear differential equation $f'''+(m+2)ff''-(2m+1)f'^2=0$ on $\mathbb{R}^+$ with the boundary conditions $f(0)=-\gamma$, $f'(\infty)=0$ and $f''(0)=-1$. This problem arises when looking for similarity solutions for boundary layer flows with prescribed heat flux. To study solutions we use some direct approach as well as blowing-up coordinates to obtain a plane dynamical system.
 1: Laboratoire de Mathématiques Informatique et Applications (LMIA) Université de Haute Alsace - Mulhouse 2: Department of Mathematics (TECHNION) Technion - Israel Institute of Technology
 Subject : Mathematics/Classical Analysis and ODEsPhysics/Mechanics/Mechanics of the fluidsEngineering Sciences/Mechanics/Fluids mechanics
 Keyword(s): Third order differential equations – boundary value problems – blowing-up coordinates – plane dynamical systems