L'attività di ricerca di chi scrive si è finora indirizzata principalmente verso l'esame dei modelli di transizione di fase, dei modelli di isteresi, e delle relative equazioni non lineari alle derivate parziali. Qui si illustrano brevemente tali problematiche, indicando alcuni degli elementi che le collegano tra di loro. Il lavoro è organizzato come segue. I paragrafi 1, 2, 3 vertono sulle transizioni di fase: si introducono le formulazioni forte e debole del classico modello di Stefan, e si illustrano alcune generalizzazioni motivate fisicamente. Nei paragrafi 4, 5, 6 si definisce il concetto di operatore di isteresi, si forniscono alcuni esempi, e si discutono alcune equazioni alle derivate parziali in cui figurano tali operatori. Le due parti sono presentate in modo da consentirne una lettura indipendente.
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