Our aim is studying differential models for phase transition problems and the related initial and boundary value problems for the partial differential equations that enter the description of such physical phenomena. In particolar, we are interested in a) phase field models with or without memory; b) solid-liquid and solid-solid phase transitions; c) thermomechanical models for shape memory alloys; d) generalized systems for phase transitions; e) extensions and generalizations of the classical Stefan problem with a special attention to the case of several phases; f) evolution equations and systems in termodynamics with a dissipative character; g) evolution systems with hysteresis effects; h) phase transition problems with discontinuous coefficients in space; i) damage and contact problems in thermomechanics. Mainly, we want to develope a theoretical analysis of qualitative and quantitative properties of the above problems: existence, uniqueness, regularity, and long time behaviour of the solutions, asymptotic analises with respect to some parameters. Moreover, we want to study the some time discretizations and prove convergence results and error estimates.
