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One-dimensional problem for heat and mass transport in oil-wax solution. (English) Zbl 1225.35259

Summary: A mathematical model of heat and mass transport in non-isothermal partially saturated oil-wax solution was formulated by A. Fasano and M. Primicerio [in: New trends in mathematical physics. In honour of the Salvatore Rionero 70th birthday. Proceedings of the international meeting, Naples, Italy, 2003. Hackensack, NJ: World Scientific. 34–44 (2005; Zbl 1088.76068)].
This paper is devoted to the study of a one-dimensional problem in the framework of that model. The existence of classical solutions in a small time interval is proved, based on the application of a fixed-point theorem to the constructed operator. The technique employed is close to the one of A. G. Petrova [Dinamika Sploshn. Sredy 58, 156-163 (1982; Zbl 0521.76083)] and A. Fasano and M. Primicerio [Free boundary problems, theory and applications, Vol. II, Proc. interdisc. Symp., Montecatini/Italy 1981, Res. Notes Math. 79, 644–657 (1983; Zbl 0511.35088)].

MSC:

35R35 Free boundary problems for PDEs
76A05 Non-Newtonian fluids
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