Abstract
In this paper a boundary problem is considered for which the boundary is to be determined as part of the solution. A time-dependent problem involving linear diffusion in two spatial dimensions which results in a moving free boundary is posed. The fundamental solution is introduced and Green’s Theorem is used to yield a non-linear system of integral equations for the unknown solution and the location of the boundary. The boundary element method is used to obtain a numerical solution to this system of integral equations which in turn is used to obtain the solution of the original problem. Graphical results for a two-dimensional problem are presented. Published in 1999 by John Wiley & Sons, Ltd.
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