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

✍ Scribed by Giulio Schimperna

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 170 KB
• Volume: 22
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19990925)22:14<1235::aid-mma82>3.0.co;2-w

✦ Synopsis

The heat di!usion in a #uid with possible phase change is studied as the boundary condition in a part of the edge of the considered region consists in another di!usion 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 where the heat conductivity goes increasing in a privileged direction. The phase-"eld 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).