Search results for "Method of matched asymptotic expansions"
showing 3 items of 3 documents
Asymptotic stability of solutions to Volterra-renewal integral equations with space maps
2012
Abstract In this paper we consider linear Volterra-renewal integral equations (VIEs) whose solutions depend on a space variable, via a map transformation. We investigate the asymptotic properties of the solutions, and study the asymptotic stability of a numerical method based on direct quadrature in time and interpolation in space. We show its properties through test examples.
Matched asymptotic solution for the solute boundary layer in a converging axisymmetric stagnation point flow
2007
Abstract A novel boundary-layer solution is obtained by the method of matched asymptotic expansions for the solute distribution at a solidification front represented by a disk of finite radius R 0 immersed in an axisymmetric converging stagnation point flow. The detailed analysis reveals a complex internal structure of the boundary layer consisting of eight subregions. The development of the boundary layer starts from the rim region where the concentration, according to the obtained similarity solution, varies with the radius r along the solidification front as ∼ln 1/3 ( R 0 / r ). At intermediate radii, where the corresponding concentration is found to vary as ∼ln( R 0 / r ), the boundary …
Nonlinear Critical Layers in Barotropic Stability
1991
Abstract Applying the method of matched asymptotic expansions (MAE) to the shallow water equations on a rotating sphere, the structure of critical layers that occur in the linear and inviscid analysis of neutral disturbances of barotropic zonal flows is investigated, assuming that the critical layers are controlled by nonlinearity rather than viscosity or nonparallel flow effects. It turns out that nonlinearity is insufficient to resolve the critical layer singularity completely. It suffices however to connect linear and nondissipative solutions across critical latitudes.