On the Computation of Free Boundaries

Abstract

Problems in which the solution of a (partial) differential equation has to satisfy certain conditions on the boundary of a prescribed domain are referred to as boundary-value problems. In many cases, however, the boundary of the domain is not known in advance but has to be determined as part of the solution. The term stationary free-boundary (SFB) is commonly used when the boundary is stationary and a steady-state exists. Moving free boundaries (MFB), on the other hand, are associated with time-dependent problems and the position of the boundary now is a function of time and space. In applications, SFB problems are usually of elliptic type, while MFB problems are often described by parabolic equations. We refer to [l] which presents a broad and detailed account of the mathematical (both analytical and numerical) solution of FB problems.