Geodesic
Analytic solution of single-phase Stefan problem
Matematičeskoe modelirovanie, Tome 20 (2008) no. 3, pp. 77-86 
È. M. Kartashov; G. S. Krotov. Analytic solution of single-phase Stefan problem. Matematičeskoe modelirovanie, Tome 20 (2008) no. 3, pp. 77-86. http://geodesic.mathdoc.fr/item/MM_2008_20_3_a6/
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     author = {\`E. M. Kartashov and G. S. Krotov},
     title = {Analytic solution of single-phase {Stefan} problem},
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     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Authors found analytic solutions of Stefan problem with different boundary conditions on $x=0$ surface by means of the method of differential rows and the method of general integral transformation. They showed the equivalence of these solutions in a confluent domain, i.e. $y(0)=0$. Authors considered a few particular cases of general solutions in dimensionless variables and drew their graphs. Authors found coefficients of proportionality in the law of moving of a boundary in the tenth decimal place.

[1] Kartashov E. M., “Analiticheskie metody resheniya kraevykh zadach nestatsionarnoi teploprovodnosti v oblastyakh s dvizhuschimisya granitsami”, Analiticheskii obzor, posvyaschennyi 275-letiyu RAN, Izvestiya RAN, Energetika, 1999, no. 5, 3–32

[2] Danilyuk I. I., “O zadache Stefana”, UMN, 40:5(245) (1985), 133–185 | MR | Zbl

[3] Kartashov E. M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel, Vysshaya shkola, M., 2001 \, 550 pp.

[4] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977

[5] Lyubov B. Ya., DAN SSSR, 68 (1949), 847 | MR | Zbl

[6] Borisov V. T., Lyubov B. Ya., Temkin D. E., “O raschete kinetiki zatverdevaniya metallicheskogo slitka pri razlichnykh temperaturnykh usloviyakh na ego poverkhnosti”, DAN SSSR, 104:2 (1955), 223–226

[7] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1962, 1100 pp. | MR

[8] Chekmareva O. M., “Po povodu zadachi Stefana v tsilindricheskoi i sfericheskoi sistemakh koordinat”, Zhurnal tekhnicheskoi fiziki, 41:5 (1971), 1071–1072