Asymptotic expansions of solutions of von Karman's swirling flow problem are considered. These expansions are used to prove the convergence of a class of approximating problems, which are set up by substituting for the infinite interval on which von Karman's problem is posed a finite but large one, and by imposing supplementary boundary conditions at the far end. The asymptotic expansions are crucial for the determination of the order of convergence. Exponential convergence is shown for well-posed approximate problems. The given approach is applicable to general autonomous nonlinear boundary value problems on infinite intervals, for which the von Karman problem may be considered as a model problem.
ASJC Scopus subject areas
- Applied Mathematics