Global solutions to phase change models with heat transfer for a class of smart materials

This paper is concerned with the global solvability of three-dimensional models for smart materials undergoing phase transitions with heat transfer. The problem is formulated within the framework of generalized standard solids by the coupling of the momentum equilibrium equation and the flow rule with the heat transfer equation. Under appropriate regularity assumptions on the initial data, a global existence result for this thermodynamically consistent system is established by using a fixed-point argument combined with energy estimates.