Inthermal equilibrium,eachphase(i.e.liquid,solidetc.) of physicalmattercomes to an end at a transitional point, or spatialinterface,called aphase boundary,due to theimmiscibilityof the matter with the matter on the other side of the boundary. This immiscibility is due to at least one difference between the two substances' corresponding physical properties. The behavior of phase boundaries has been a developing subject of interest and an active interdisciplinary research field, calledinterface science,for almost two centuries, due partly to phase boundaries naturally arising in many physical processes, such as thecapillarity effect,the growth ofgrain boundaries,the physics ofbinary alloys,and the formation ofsnow flakes.
One of the oldest problems in the area dates back to Lamé and Clapeyron[1]who studied the freezing of the ground. Their goal was to determine the thickness of solid crust generated by the cooling of a liquid at constanttemperaturefilling thehalf-space.In 1889, Stefan, while working on the freezing of the ground developed these ideas further and formulated the two-phase model which came to be known as theStefan Problem.[2]
The proof for the existence and uniqueness of a solution to theStefan problemwas developed in many stages. Proving the general existence and uniqueness of the solutions in the case ofwas solved byShoshana Kamin.
References
edit- ^G. Lamé,B. P. Clapeyron,Memoire sur la solidification par refroiddissement d'un globe solide, Ann. Chem. Physics, 47, 250–256 (1831).
- ^J. Stefan,Über einige Probleme der Theorie der Warmeleitung, S.-B Wien Akad. Mat. Natur, 98, 173–484, (1889).
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