@article{d984a2ec2e3249b7805c17157dd85eb7,
title = "EXACT AND APPROXIMATE SOLUTIONS TO THE STEFAN PROBLEM IN ELLIPSOIDAL COORDINATES",
abstract = "In this paper, we present exact and approximate solutions of the Stefan problems in ellipsoidal coordinates. We consider two models of electrical contact heating for melting process. The first problem describes the contact heating for liquid and solid zones based on the two-phase Stefan problem, where time t is present as a parameter. Contact heating including softening processes are described by a mathematical model based on the three-phase Stefan problem for the ellipsoidal heat equation.",
keywords = "Electrical contact heating, Heat balance integral method, Joule heating, Softening stage, Stefan problems",
author = "Kassabek, {S. A.} and Kharin, {S. N.} and D. Suragan",
note = "Funding Information: The authors were supported by the Nazarbayev University Program 091019CRP2120 {"}Centre for Interdisciplinary Studies in Mathematics (CISM){"} and the second author was supported by the grant no. AP09258948 {"}A free boundary problems in mathematical models of electrical contact phenomena{"} and by the grant no. OR11466188 ({"}Dynamical Analysis and Synchronization of Complex Neural Networks with Its Applications{"}). Funding Information: Supported by the ISAAC (International Society for Analysis, its Applications and Computation) and by the Kazakhstan Mathematical Society Publisher Copyright: {\textcopyright} 2022, Eurasian Mathematical Journal.All Rights Reserved.",
year = "2022",
doi = "10.32523/2077-9879-2022-13-3-51-66",
language = "English",
volume = "13",
pages = "51--66",
journal = "Eurasian Mathematical Journal",
issn = "2077-9879",
publisher = "L. N. Gumilyov Eurasian National University",
number = "3",
}