A nonlocal quasilinear multi-phase system with nonconstant specic heat and heat conductivity

In this paper, the authors prove the existence and global boundedness from above for a solution to an integrodierential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integrodifferential inclusion governing the (vectorial) phase-parameter dynamics. The specic heat and the heat conductivity k are allowed to depend both on the order parameter and on the absolute temperature of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions.