Existence for a model arising from the in situ vitrification process
type: Item
instance of: scholarly article
title: Existence for a model arising from the in situ vitrification process
zbMATH Open document ID: 1011.35135
DOI: 10.1016/S0022-247X(02)00112-9
author: Xiangsheng Xu
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: 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.
reviewed by: David S. Boukal
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 1836757
zbMATH Keywords: capacity solution
zbMATH Keywords: Hölder continuity
MaRDI profile type: Publication
cites work: Existence of generalized weak solutions to a model for in situ vitrification
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cites work: A compactness theorem and its application to a system of partial differential equations
cites work: The thermistor problem with conductivity vanishing for large temperature
cites work: Partial regularity of solutions to a class of degenerate systems
cites work: A P-laplacian problem in L1with nonlinear boundary conditions
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description: scientific article; zbMATH DE number 1836757