Diffusion with prescribed convection in fissured media. (English) Zbl 0723.76088
(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)].}
{Remark: Cf. also M. Böhm and the second author [SIAM J. Math. Anal. 16, 500-509 (1985; Zbl 0613.76103)].}
Reviewer: M.Kracht (Düsseldorf)
MSC:
76R50 | Diffusion |
76R05 | Forced convection |
35D05 | Existence of generalized solutions of PDE (MSC2000) |
76S05 | Flows in porous media; filtration; seepage |
80A20 | Heat and mass transfer, heat flow (MSC2010) |
80A22 | Stefan problems, phase changes, etc. |
35B65 | Smoothness and regularity of solutions to PDEs |