Existence for a model arising from the in situ vitrification process
The author modifies an earlier model of in situ vitrification [see \textit{R. F. Gariepy, M. Shillor}, and \textit{X. Xu}, Eur. J. Appl. Math. 9, No. 6, 543-559 (1998; Zbl 0939.35197)] to account for time-dependent case. He provides a classical formulation of the model and shows that under mild conditions the resulting system of PDEs has a ``capacity solution'' in the sense of \textit{X. Xu} [Differ. Integral Equ. 9, No. 1, 119-136 (1996; Zbl 0843.35049) and Proc. R. Soc. Edinb., Sect. A 124, No. 1, 1-21 (1994; Zbl 0807.35143)]. The existence of this solution requires mild assumptions on the data as well as on electrical and temperature-dependent heat conductivities, and it is established by constructing a sequence of approximate solutions.
scientific article; zbMATH DE number 1836757