On a Similarity Boundary Layer Equation

  • B. Brighi

    Université de Haute Alsace, Mulhouse, France


The purpose of this paper is to study the autonomous third order nonlinear differential equation f+m+12ffmf2=0f'''+ \frac{m+1}{2} f f'' – mf'^2 = 0 on (0,)(0, \infty), subject to the boundary conditions f(0)=aR,f(0)=1f(0) = a \in \mathbb R, f'(0) = 1 and f(t)0f'(t) \rightarrow 0 as tt \rightarrow \infty. This problem arises when looking for similarity solutions to problems of boundary-layer theory in some contexts of fluids mechanics, as free 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 studying existence or non-existence and uniqueness or non-uniqueness of solutions according to the values of the real parameter m. In particular, we will emphasize similarities and differences between the cases a=0a = 0 and a0a \neq 0 in the boundary condition f(0)=af(0) = a.

Cite this article

B. Brighi, On a Similarity Boundary Layer Equation. Z. Anal. Anwend. 21 (2002), no. 4, pp. 931–948

DOI 10.4171/ZAA/1118