TY - JOUR

T1 - Justification of a quasistationary approximation for the stefan problem

AU - Solonnikov, V. A.

AU - Forolova, E. V.

PY - 2008/8/1

Y1 - 2008/8/1

N2 - Unique solvability of the one-phase Stefan problem with a small multiplier ε at the time derivative in the equation is proved on a certain time interval independent of ε for ε (0, ε0). The solution to the Stefan problem is compared with the solution to the Hele-Show problem, which describes the process of melting materials with zero specific heat ε and can be regarded as a quasistationary approximation for the Stefan problem. It is shown that the difference of the solutions has order script O sign (ε) + script O sign (e-ct/ε). This provides a justification of the quasistationary approximation. Bibliography: 23 titles. © 2008 Springer Science+Business Media, Inc.

AB - Unique solvability of the one-phase Stefan problem with a small multiplier ε at the time derivative in the equation is proved on a certain time interval independent of ε for ε (0, ε0). The solution to the Stefan problem is compared with the solution to the Hele-Show problem, which describes the process of melting materials with zero specific heat ε and can be regarded as a quasistationary approximation for the Stefan problem. It is shown that the difference of the solutions has order script O sign (ε) + script O sign (e-ct/ε). This provides a justification of the quasistationary approximation. Bibliography: 23 titles. © 2008 Springer Science+Business Media, Inc.

UR - http://www.scopus.com/inward/record.url?scp=51749097972&partnerID=8YFLogxK

U2 - 10.1007/s10958-008-9091-6

DO - 10.1007/s10958-008-9091-6

M3 - Article

AN - SCOPUS:51749097972

VL - 152

SP - 741

EP - 768

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -