Abstract
A one-dimensional mathematical model for a process of solidification of a binary alloy in the presence of an electric field is studied. A situation in which the thermal properties of each phase are different and the latent heat is non-zero is considered. A quasi-static approximation for the thermal and electric fields is used. Local existence and uniqueness of a classical solution to the resulting free boundary problem are proved for two kinds of boundary conditions. Moreover, under particular hypotheses, the monotonicity of the free boundary and the global existence of the solution is proved.
Sommario
Si studia un modello matematico unidimensionale per un processo di solidificazione di una lega binaria in presenza di un campo elettrico. Si considera una situazione in cui le proprietà termiche di ogni fase sono differenti e il calore latente è non nullo. Si usa una approssimazione quasi-statica per i campi elettrico e termico. Si dimostra l'esistenza locale e l'unicità di una soluzione classica per il problema di frontiera libera risultante con due tipi di condizioni di bordo. Inoltre si dimostra, sotto particolari ipotesi, la monotonia della frontiera libera e l'esistenza di soluzione globale.
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Stampella, M. A mathematical model for an alloy solidification problem in the presence of an electric field. Meccanica 26, 211–219 (1992). https://doi.org/10.1007/BF00430938
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DOI: https://doi.org/10.1007/BF00430938