Uniqueness in a melting slab with space- and time-dependent heating
Bruno A. Boley · Quarterly of Applied Mathematics · 1970
Conditions for uniqueness of solution are derived for a slab which melts under an applied heat input dependent both on time and on the melted depth, the melted material being instantaneously removed. Some examples are constructed in which more than one solution is exhibited as well as one in which no melting solution exists. A theorem demonstrating monotonic dependence of solution on boundary data under certain conditions is proved.