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- W1566455073 abstract "We establish the existence and partial regularity of a capacity solution to a coupled, degenerate, strongly nonlinear system of PDE's which models the melting of a solid due to volume electric heating. The system generalizes the usual Stefan problem, the evolutionary thermistor problem, and the spot welding problem. We allow temperature dependence for the electrical conductivity---which may lead to degeneracy---and take fully into account the flow of the fluid, which we model with the Navier-Stokes system. Existence is proved by considering a sequence of approximate problems, for which a priori estimates are obtained. Then the limit provides a capacity solution for the original problem. The approximate problems are obtained by smoothing, time-retardation and penalization. Of special interest is the fact that the set where the material is above its melting temperature is open, since only there the Navier-Stokes equations hold. The question of the behavior of solutions in mushy regions, regions where the temperature is identically the melting temperature, is left open." @default.
- W1566455073 created "2016-06-24" @default.
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- W1566455073 date "1997-01-01" @default.
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- W1566455073 title "The Stefan problem with convection and Joule's heating" @default.
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- W1566455073 doi "https://doi.org/10.57262/ade/1366741153" @default.
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