Geodesic
On conditions for the existence of a classical solution of the modified Stefan problem (the Gibbs–Thomson law)
Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 221-246 
E. V. Radkevich. On conditions for the existence of a classical solution of the modified Stefan problem (the Gibbs–Thomson law). Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 221-246. http://geodesic.mathdoc.fr/item/SM_1993_75_1_a12/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Sufficient conditions close to necessary are obtained for the existence of a solution (unique for $\sigma>0$ and $\beta>0$) of a solution of the modified Stefan problem on a small time interval.

[1] Radkevich E. V., “O razreshimosti obschikh nestatsionarnykh zadach so svobodnoi granitsei”, DAN SSSR, 288:5 (1986), 1094–1099 | MR | Zbl

[2] Radkevich E. V., Melikulov A. S., Kraevye zadachi so svobodnoi granitsei, FAN, Tashkent, 1988 | MR | Zbl

[3] Radkevich E. V., “Usloviya suschestvovaniya perekhodnoi zony i vyrozhdennaya zadacha Florina”, Kraevye zadachi dlya uravn. s chastn. proizvodnymi, Sb. nauch. tr. Matem. in-ta SO AN SSSR, Novosibirsk, 1987, 80–124

[4] Radkevich E. V., “Ob operatornykh puchkakh kontaktnoi zadachi Stefana”, Matem. zametki, 47:2 (1990), 89–101 | MR | Zbl

[5] Radkevich E. V., “O spektre puchka zadachi Verigina”, Matem. zametki, 49:3 (1991), 77–90 | MR | Zbl

[6] Radkevich E. V., “Ob usloviyakh suschestvovaniya klassicheskogo resheniya kontaktnoi zadachi Stefana”, Matem. sb., 181:4 (1990), 464–489 | MR | Zbl

[7] Golovkin K. K., Solonnikov V. A., “Ob otsenkakh operatorov svertki”, Zap. nauch. sem. LOMI, 1988, no. 7, 6–86 | MR

[8] Solonnikov V. A., “Otsenki reshenii nekotorykh nekoertsitivnykh nachalno-kraevykh zadach s pomoschyu teoremy o multiplikatorakh v integralakh Fure - Laplasa”, Zap. nauch. sem. LOMI, 1987, 220–227

[9] Hanzawa Ei-Ichi., “Classical solutions of the Stefan problem”, Tôhoku Math. J., 33:3 (1981), 297–335 | DOI | MR | Zbl

[10] Meirmanov A. M., Zadacha Stefana, Nauka, Novosibirsk, 1986 | MR | Zbl

[11] Caginalp G., “Mathematical models of phase boundaries”, Symp. on Materiel Instabilites in Continuum Mechanics, Heriot-Walt Univ. (1985–1986), ed. J. Ball, Oxford Science Publ., 1988, 39–50 | MR

[12] Caroli B., Caroli C, Misbah C, Roulet B., “The Gibbs Thomson law”, J. Phys., 48 (1987), 547

[13] Caginalp G., “The role of microscopic behavior of a phase boundary”, Ann. Phys., 172 (1986), 136–155 | DOI | MR | Zbl

[14] Radkevich E. V., Melikulov A. S., Zadachi so svobodnoi granitsei, FAN, Tashkent, 1991 | Zbl

[15] Radkevich E. V., “Popravka Gibbsa - Tomsona i suschestvovanie klassicheskogo resheniya modifitsirovannoi zadachi Stefana”, DAN SSSR, 315:6 (1991)