The conserved Penrose-Fife system with temperature-dependent memory

A nonlinear parabolic system of Penrose-Fife type with a singular evolution term, arising from modelling dynamic phenomena of the non-sothermal diffusive phase separation, is studied. Here, we consider the evolution of a material in which the heat flux is a superposition of two contributions: one part is proportional to the spacial gradient of the inverse of the absolute temperature \theta, while the other agrees with the Gurtin-Pipkin law, introduced in the theory of materials with termal memory. The phase transition here is described through the evolution of the conserved parameter \chi, wich may represent the concentration of some substance. It is shown that an initial-boundary value problem for the resulting state equation has a unique solution.