The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (257 KB) | Metadata | Table of Contents | ZAA summary
Volume 21, Issue 4, 2002, pp. 931–948
DOI: 10.4171/ZAA/1118

Published online: 2002-12-31

On a Similarity Boundary Layer Equation

B. Brighi[1]

(1) Université de Haute Alsace, Mulhouse, France

The purpose of this paper is to study the autonomous third order nonlinear differential equation $f'''+ \frac{m+1}{2} f f'' – mf'^2 = 0$ on $(0, \infty)$, subject to the boundary conditions $f(0) = a \in \mathbb R, f'(0) = 1$ and $f'(t) \rightarrow 0$ as $t \rightarrow \infty$. 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 $a = 0$ and $a \neq 0$ in the boundary condition $f(0) = a$.

Keywords: Third order differential equation, boundary layer, similarity solution

Brighi B.: On a Similarity Boundary Layer Equation. Z. Anal. Anwend. 21 (2002), 931-948. doi: 10.4171/ZAA/1118