A reaction–diffusion system approximation to the two-phase Stefan problem

✍ Scribed by D. Hilhorst; M. Iida; M. Mimura; H. Ninomiya

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 475 KB
• Volume: 47
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00224-3

✦ Synopsis

It is well known that the classical two-phase Stefan problem, which is an orderpreserving system, can be regarded as a singular limit of a phase field model. However the rigorous analysis of the phase field model is not easy, because it is not an order-preserving system and also is strongly coupled. In this article it is clarified that the two-phase Stefan problem can actually be regarded as a singular limit of an order-preserving reaction-diffusion system which is also weakly coupled. This system is expected to bring new effective approaches to the study of the two-phase Stefan problem.