A stefan-like problem with a kinetic condition and surface tension effects

Authors:
S. H. Doole
Affiliations:
Department of Engineering Mathematics Bristol University, Queen's Building University Walk, Bristol BS8 1TR, U.K.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1996

Citing 5
Cited 0

An atlas of functions

An atlas of functions
The Stefan problem with kinetic condition at the free boundary

SIAM Journal on Mathematical Analysis
Curvature-driven flows: a variational approach

SIAM Journal on Control and Optimization
On a dissolution-growth problem with surface tension in the neighborhood of a stationary solution

SIAM Journal on Mathematical Analysis
Weakly nonlinear stability analyses of prototype reaction-diffusion model equations

SIAM Review

Quantified Score

Hi-index	0.98

Visualization

Abstract

A two-dimensional, one phase Stefan-type problem is described as a model for an industrial erosion/deposition process, which includes surface tension effects and a kinetic condition at the free boundary. Special solutions (similarity and 'traveling wave') are considered. The stability of the free boundary of these special solutions is proved within the class of planar solutions, as is their linear stability as solutions of the full problem. The role of surface energy and the interaction rate in stabilizing solutions corresponding to deposition is discussed.