The free-boundary Brakke flow

THE STEFAN PROBLEM WITH KINETIC FUNCTIONS AT THE FREE BOUNDARY

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

Boundary layer flow beneath a uniform free stream permeable continuous moving surface in a nanofluid

The main purpose of this paper is to introduce a boundary layer analysis for the fluid flow andheat transfer characteristics of an incompressible nanofluid flowing over a permeable isothermalsurface moving continuously. The resulting system of non-linear ordinary differential equations issolved numerically using the fifth–order Runge–Kutta method with shooting techniques usingMatlab and Maple s...

Mean curvature flow with free boundary outside a hypersphere

The purpose of this paper is twofold: first, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary exists globally in time and converges to a minimal surface, and second, to illustrate the application of Killing vector fields in the preservation of graphicality for the mean curvature flow with free boundary. To this en...

Analysis of a one-dimensional free boundary flow problem

A one-dimensional free surface problem is considered. It consists in Burgers’ equation with an additional diffusion term on a moving interval. The well-posedness of the problem is investigated and existence and uniqueness results are obtained locally in time. A semi-discretization in space with a piecewise linear finite element method is considered. A priori and a posteriori error estimates are...

Myron Kendall Brakke: 1921 to 2007.