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September  2002, 1(3): 313-325. doi: 10.3934/cpaa.2002.1.313

The evolution thermistor problem with degenerate thermal conductivity

María Teresa González Montesinos 1, and  Francisco Ortegón Gallego 2,

1. 

Departmento de Matemáticas, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, 11002 Cádiz, Spain
2. 

Departamento de Matemáticas, Universidad de Cádiz, CASEM, Campus del Río San Pedro, 11510 Puerto Real, Cádiz, Spain

Received  June 2001 Revised  January 2002 Published  June 2002

The existence of a weak solution for the time dependent thermistor problem with degenerate thermal conductivity is proved in this work. The main difficulties of this problem lies on the absence of space estimates for the temperature and time estimates for the electrical potential.
Keywords: Sobolev spaces., weak solutions, nonlinear parabolic equations of degenerate type, Thermistor problem.
Mathematics Subject Classification: 35M10, 35J60, 35K6.
Citation: María Teresa González Montesinos, Francisco Ortegón Gallego. The evolution thermistor problem with degenerate thermal conductivity. Communications on Pure & Applied Analysis, 2002, 1 (3) : 313-325. doi: 10.3934/cpaa.2002.1.313
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