Abstract
The paper describes two types of regularization to the basic quasistatic double-well potential problem in one space dimension. One model features a spatially nonlocal term while the other incorporates the use of an order parameter. Some basic existence and regularity results for these modified models are derived and some numerical calculations that show hysteresis and motion of phase boundaries are presented.
Sommario
Il lavoro descrive due tipi di regolarizzazione del problema quasistatico per un potenziale con due minimi in una dimensione. Un modello evidenzia caratteri di non località spaziale, mentre l'altro conduce ad una teoria con parametro d'ordine. Si derivano alcuni risultati di esistenza e regolarità e si presentano alcuni studi numerici che mostrano l'isteresi e il moto delle frontiere tra le fasi.
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Brandon, D., Lin, T. & Rogers, R.C. Phase transitions and hysteresis in nonlocal and order-parameter models. Meccanica 30, 541–565 (1995). https://doi.org/10.1007/BF01557084
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DOI: https://doi.org/10.1007/BF01557084