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We study the thermistor problem with Robin boundary condition for the temperature. A theorem of existence is proved using the compensated compactness method. For the one-dimensional case a result of non-existence and non-uniqueness is also given.
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Giovanni Cimatti, The thermistor problem with Robin boundary condition. Rend. Sem. Mat. Univ. Padova 135 (2016), pp. 175–193DOI 10.4171/RSMUP/135-10