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Volume 7, Issue 1
Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem

Chen Xinfu

J. Part. Diff. Eq.,7(1994),pp.19-34

Published online: 1994-07

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  • Abstract
A thermistor is an electric circuit device made of ceramic material whose electric conductivity depends on the temperature. If the only heat source is the electric heating, the temperature and the electric potential satisfy a nonlinear elliptic system which is also degenerate if the electric conductivity is not uniformly bounded from above or away from zero. Under general boundary conditions, we establish existence and Hölder continuity of solutions of such a nonlinear nonuniformly elliptic system. When the elechic conductivity linearly depends on the temperature, we provide a non-uniqueness and non-existence example.
  • Keywords

Thermistor elliptic system nonlinear nonuniformly elliptic mixed boundary value problem

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@Article{JPDE-7-19, author = {Chen Xinfu}, title = {Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem}, journal = {Journal of Partial Differential Equations}, year = {1994}, volume = {7}, number = {1}, pages = {19--34}, abstract = { A thermistor is an electric circuit device made of ceramic material whose electric conductivity depends on the temperature. If the only heat source is the electric heating, the temperature and the electric potential satisfy a nonlinear elliptic system which is also degenerate if the electric conductivity is not uniformly bounded from above or away from zero. Under general boundary conditions, we establish existence and Hölder continuity of solutions of such a nonlinear nonuniformly elliptic system. When the elechic conductivity linearly depends on the temperature, we provide a non-uniqueness and non-existence example.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5670.html} }
TY - JOUR T1 - Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem AU - Chen Xinfu JO - Journal of Partial Differential Equations VL - 1 SP - 19 EP - 34 PY - 1994 DA - 1994/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5670.html KW - Thermistor KW - elliptic system KW - nonlinear KW - nonuniformly elliptic KW - mixed boundary value problem AB - A thermistor is an electric circuit device made of ceramic material whose electric conductivity depends on the temperature. If the only heat source is the electric heating, the temperature and the electric potential satisfy a nonlinear elliptic system which is also degenerate if the electric conductivity is not uniformly bounded from above or away from zero. Under general boundary conditions, we establish existence and Hölder continuity of solutions of such a nonlinear nonuniformly elliptic system. When the elechic conductivity linearly depends on the temperature, we provide a non-uniqueness and non-existence example.
Chen Xinfu. (1970). Existence and Regularity of Solutions of a Nonlinear Nonuniformly Elliptic System Arising from a Thermistor Problem. Journal of Partial Differential Equations. 7 (1). 19-34. doi:
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