Abstract
This article addresses the mathematical analysis of a model for the irreversible solidification process of certain materials by taking in consideration the effects of natural convection in molten regions. Such a model consists of a highly nonlinear system of partial differential equations coupled to a doubly nonlinear differential inclusion. The existence of weak–strong solutions for the system is proved, and certain mathematical effects of advection on the regularity of the solutions are discussed.
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Boldrini, J.L., de Miranda, L.H. & Planas, G. A Mathematical analysis of fluid motion in irreversible phase transitions. Z. Angew. Math. Phys. 66, 785–817 (2015). https://doi.org/10.1007/s00033-014-0434-5
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DOI: https://doi.org/10.1007/s00033-014-0434-5