A hysteresis approach to phase-field models
The phase-field model is described by a system of equations for an order parameter \(w\) and the absolute temperature \(T\) involving hysteresis operators, that is to say, loosely speaking, functions of sets. The differential inclusion is converted into an inequality, the solution of which is defined as a set function. Uniqueness and existence theorems are stated, the solution is constructed by a successive approximation, and its stability is analyzed. There is thermodynamic consistency.
scientific article; zbMATH DE number 1389678