One-dimensional problem for heat and mass transport in oil-wax solution (Q2504823)

Summary: A mathematical model of heat and mass transport in non-isothermal partially saturated oil-wax solution was formulated by \textit{A. Fasano} and \textit{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 \textit{A. G. Petrova} [Dinamika Sploshn. Sredy 58, 156-163 (1982; Zbl 0521.76083)] and \textit{A. Fasano} and \textit{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)].