Weak solution to a phase-field transmission problem in a concentrated capacity

Abstract

The heat diffusion in a fluid with possible phase change is studied as the boundary condition in a part Γ of the edge of the considered region consists in another diffusion equation for the traces of the unknowns. This feature, called concentrated capacity, arises as the limit situation of a family of heat transmission problems between the original body and an outer neighbourhood of Γ where the heat conductivity goes increasing in a privileged direction. The phase-field model is adopted for the physical description. The concentrated capacity formulation is directly addressed in its variational setting and an existence and uniqueness theorem is proved by means of approximation techniques for parabolic systems (Faedo–Galerkin scheme, Yosida regularization). Copyright © 1999 John Wiley & Sons, Ltd.