Existence of generalized weak solutions to a model for in situ vitrification

Autor:	Xiangsheng Xu, R. F. Gariepy, Meir Shillor
Rok vydání:	1998
Předmět:	Materials science Electrical resistivity and conductivity Applied Mathematics Degenerate energy levels Stefan problem Free boundary problem Vitrification Mechanics Electric potential Degeneracy (mathematics) Joule heating
Zdroj:	European Journal of Applied Mathematics. 9:543-559
ISSN:	1469-4425 0956-7925
DOI:	10.1017/s0956792598003593
Popis:	We prove the existence of generalized weak solutions of a new model for the process of in situ vitrification. The model describes the steady process of vitrification of soil, i.e. the melting of soil by means of electrical current and subsequent solidification as a rock. This is the core of a new technology developed to treat buried low-level radioactive or toxic waste. It is a free boundary problem consisting of a degenerate elliptic equation for the electric potential coupled with a stationary Stefan problem for melting the soil, which results from the Joule heating. The degeneracy reflects the smallness of the ratio of the electrical conductivity of the soil to that of the molten rock. The existence result is proved by considering a sequence of approximate nondegenerate problems, obtaining the necessary a priori estimates and passing to the limit. We also establish a sufficient condition for the solution to exhibit a molten region.
Databáze:	OpenAIRE
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