Weak solution to some Penrose-Fife phase-field systems with temperature-dependent memory
The authors consider a phase-field model of Penrose-Fife type in which the heat flux contains two distinct parts: one part that is proportional to the spatial gradient of the inverse temperature, and another one that depends on the past history of the temperature gradient. The main result of the paper is concerned with the existence and uniqueness of weak (variational) solutions to an initial-boundary value problem for a system of integro-partial differential equations describing the above model. The approach is based on the study of a related approximating problem, followed by passage to the limit. This requires establishing delicate estimates for the approximate solutions. Although the analysis is completed for a bounded three-dimensional domain, it is conjectured that the theory holds in any spatial dimension.
system of integro-partial differential equations
scientific article; zbMATH DE number 1130543