Back to Search
Start Over
Local well-posedness and Global stability of the Two-Phase Stefan problem
- Publication Year :
- 2016
-
Abstract
- The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed of two regions separated by an a priori unknown moving boundary which is transported by the difference (or jump) of the normal derivatives of the temperature in each phase. We establish local-in-time well-posedness and a global-in-time stability result for arbitrary sufficiently smooth domains and small initial temperatures. To this end, we develop a higher-order energy with natural weights adapted to the problem and combine it with Hopf-type inequalities. This extends the previous work by Hadzic and Shkoller [31,32] on the one-phase Stefan problem to the setting of two-phase problems, and simplifies the proof significantly.<br />Comment: 58 pages, 1 figure
- Subjects :
- Mathematics - Analysis of PDEs
35Q79, 35B40, 35B65, 35M30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1607.00681
- Document Type :
- Working Paper