On similarity solutions for boundary layer flows with prescribed heat flux

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.