(Authors’ summary.) A system consisting of an ordinary differential equation coupled to a nonsymmetric degenerate elliptic equation provides a model for heat transfer with phase change in a fissured medium, a collection of material blocks separated by a system of fissures, when a fluid of prescribed velocity transports heat within the fissures. Additional transport in the fissures occurs by diffusion, and phase changes can occur independently in the two components along respective free-boundaries. With the physically appropriate initial and boundary conditions, the system is shown to be a well-posed problem; special regularity properties of the solution will be established.
{Remark: Cf. also M. Böhm and the second author [SIAM J. Math. Anal. 16, 500-509 (1985; Zbl 0613.76103)].}