We consider a problem related to resistance spot welding. The mathematical model describes the equilibrium state of an elastic, cracked body subjected to heat transfer and electroconductivity and can be viewed as an extension to the classical thermistor problem. We prove existence of a solution in Sobolev spaces.
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Dietmar Hömberg, Jan Sokolowski, Alexander Khludnev, Quasistationary problem for a cracked body with electrothermoconductivity. Interfaces Free Bound. 3 (2001), no. 2, pp. 129–142DOI 10.4171/IFB/36