Geodesic
Boundary integral equations of the Stefan problem in terms of the time of phase transition
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 3-19

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In this paper, a new numerical method for solving the Stefan problem based on the time function of phase transitions is considered. A nonlinear integral equation of minimal dimension is obtained and an efficient numerical method for solving this equation is proposed. The method is tested on important problems of thawing of frozen soils with various methods of thermal action.
Keywords: Stefan problem, integral equation, numerical method, soil thawing. 
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     author = {R. V. Harutyunyan},
     title = {Boundary integral equations of the {Stefan} problem in terms of the time of phase transition},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {192},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_192_a0/}
}
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R. V. Harutyunyan. Boundary integral equations of the Stefan problem in terms of the time of phase transition. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 3-19. http://geodesic.mathdoc.fr/item/INTO_2021_192_a0/