In this paper we examine two problems in steady incompressible viscous flow with a view to generating high-order perturbation solutions as regular expansions in powers of the Reynolds number. Thus, computer-algebra techniques are used to study the motions produced (a) by a Landau momentum source placed at the centre of a fluid-filled spherical shell, and (b) by a rotating sphere in both unbound...

Ahstraet-A linear perturbation method is used to solve the two-dimensional heat conduction problem in which a liquid, initially at the melting temperature, becomes solidified by heat transfer to a plane mold the temperature of which is approximately uniform, but contains a small sinusoidal perturbation in one space dimension. Results are obtained for the consequent sinusoidal perturbation in th...

This paper presents two approaches to characterize the dynamics of weight space probability density starting from a master equation. In the rst, we provide a class of algorithms for which an exact evaluation of the integrals in the master equation is possible. This enables the time evolution of the density to be calculated at each time step without approximation. In the second, we expand earlie...

In this work we present a general regularity result for small perturbation solutions of elliptic equations. Our approach was motivated by the analysis of flat level sets in Ginzburg-Landau phase transitions models, which were considered in Savin (2003). When dealing with uniformly elliptic equations of the form (1), the classical approach to regularity is to differentiate the equation with resp...