Global stability and decay for the classical Stefan problem

TY - UNPB

T1 - Global stability and decay for the classical Stefan problem

AU - Hadzic, Mahir

AU - Shkoller, Steve

PY - 2012/12/6

Y1 - 2012/12/6

N2 - The classical one-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 whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities.

AB - The classical one-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 whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities.

KW - math.AP

KW - 35R35, 35B65, 35K05, 80A22

M3 - Preprint

VL - N/A

SP - N/A

BT - Global stability and decay for the classical Stefan problem

PB - arXiv

ER -