关于一般相似边界层方程
On a general similarity boundary layer equation
摘要：
本文研究了微分方程$f'''+ff''+g(f')=0$在$[0,\infty)$上的解，满足边界条件$f(0)=α$，$f'(0)=β\geq 0$，$f'(\infty)=ł$，其中$g$是给定的连续函数.这个一般的边值问题包括Falkner-Skan情况，并且可以应用于例如多孔介质中的自由对流或混合对流，或者在边界层近似的上下文中与拉伸壁相邻的流动。在对函数$g$的一些假设下，证明了该问题的凹解或凸解的存在唯一性。我们还给出了解的不存在性和渐进性的一些结果。
英文摘要：
In this paper we are concerned with the solutions of the differential equation $f'''+ff''+g(f')=0$ on $[0,\infty)$, satisfying the boundary conditions $f(0)=α$, $f'(0)=β\geq 0$, $f'(\infty)=ł$, and where $g$ is some given continuous function. This general boundary value problem includes the Falkner-Skan case, and can be applied, for example, to free or mixed convection in porous medium, or flow adjacent to stretching walls in the context of boundary layer approximation. Under some assumptions on the function $g$, we prove existence and uniqueness of a concave or a convex solution. We also give some results about nonexistence and asymptotic behaviour of the solution.
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