Existence and regularity theorems for a two-phase degenerate stefan problem with convection

Abstract

Existence of a classical solution is demonstrated for an one-dimensional two-phase Stefan problem in which the spccilic heat may oscillate wildly near the melting temperature 0 in the sense that it is unbounded above and it is not bounded away from zero in a neighborhood of 0. The convective terms involved also display some type of singularity.

Keywords:

• degenerate Stefan problem
• regularity of the free boundary
• maximum principle
• classical solutions