The thermistor problem with conductivity vanishing for large temperature

DOI10.1017/S0308210500029164zbMath0807.35143MaRDI QIDQ4294341

Xiangsheng Xu

Publication date: 1 March 1995

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

weak solutiondistributioncapacity solutionsystem of elliptic-parabolic equations

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs of mixed type (35M10) Degenerate elliptic equations (35J70)

Related Items (13)

Dynamic thermoviscoelastic thermistor problem with contact and nonmonotone friction ⋮ Unnamed Item ⋮ Local partial regularity theorems for suitable weak solutions of a class of degenerate systems ⋮ Capacity solution for a perturbed nonlinear coupled system ⋮ Existence of a capacity solution to a nonlinear parabolic-elliptic coupled system in anisotropic Orlicz-Sobolev spaces ⋮ Optimal control of a thermistor problem with vanishing conductivity ⋮ Existence of a solution for a thermoelectric model with several phase changes and a Carathéodory thermal conductivity ⋮ Existence for the thermoelastic thermistor problem ⋮ On the existence of solutions for a strongly degenerate system ⋮ Existence of capacity solution for a perturbed nonlinear coupled system ⋮ Existence for the thermoviscoelastic thermistor problem ⋮ Existence for a model arising from the in situ vitrification process ⋮ Numerical analysis of the quasistatic thermoviscoelastic thermistor problem

Cites Work

• Unnamed Item
• Oscillations and concentrations in weak solutions of the incompressible fluid equations
• Existence of a solution to the Stefan problem with Joule's heating
• Existence results for a nonlinear elliptic system modeling a temperature dependent electrical resistor
• A nonlinear theory of generalized functions.
• The thermistor problem for conductivity which vanishes at large temperature
• Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions
• A Bound for the Temperature in the Thermistor Problem
• $C^\alpha (\bar \Omega )$ Solutions of a Class of Nonlinear Degenerate Elliptic Systems Arising in the Thermistor Problem
• A Degenerate Stefan-Like Problem with Joule’s Heating
• A strongly degenerate system involving an equation of parabolic type and an equation of elliptic type

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