Abstract
Local continuity is established for locally bounded, weak solutions to a doubly non-linear parabolic equation that models the temperature of a material undergoing a multi-phase transition. The enthalpy, as a maximal monotone graph of the temperature, is allowed to possess several jumps and/or infinite derivatives at the transition temperatures. The effect of the p -Laplacian-type diffusion is also considered. As an application, we demonstrate a continuity result for the saturation in the flow of two immiscible fluids through a porous medium, when irreducible saturation is present.
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