ON THE STABILITY OF THE SURFACE SEPARATING TWO HOMOGENEOUS MEDIA WITH DIFFERENT THERMAL CONDUCTIVITIES

§0. Introduction In some questions rolated to the earth science the following problem arises: asolid body Ω Js scparated into two subregions Ω1 and Ω2, the second strictly contained in Ω, both made of homogeneous isotropic materials with given （constant） thermal conductivities α1 and α2. From the knowledge of the temperatudre u0 and the heat flux u1 on the boundary （?）Ω of Ω, it is required to determine the position and the shape of the hidden region Ω2, i.e. to identify the surface ∑ which separates Ω1 and Ω2.