Free Boundary Problems and their Stabilisation
Free boundary problems (FBPs) are those in which some partial differential equations have to be solved in a region with a boundary whose position is to be found as part of the problem. This article will briefly review some of the theory and folklore concerning such problems and their stabilisation with the aim of highlighting the major open problems that currently confront mathematicians working in the area. It is a subject with which Prof. Hoffmann has been intimately involved over the past three decades and it is a pleasure to acknowledge the contributions he has made to our understanding of problems ranging from the Stefan problem, which created so much excitement in the 1970’s, to FBPs in superconductivity which are currently ”all the rage”. Of course I must also include Prof. Hoffmann’s involvement with the more political applications of ”les frontières libres”.
KeywordsFree Boundary Free Boundary Problem Stefan Problem Free Boundary Condition Mushy Region
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