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

It is well known that the classical two-phase Stefan problem, which is an o rder-preserving system, can be regarded as a singular limit of a phase fiel d 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 act ually be regarded as a singular limit of an order-preserving reaction-diffu sion system which is also weakly coupled. This system is expected to bring new effective approaches to the study of the two-phase Stefan problem.