Dynamics of a~free boundary in a~binary medium with variable thermal conductivity
Matematičeskie zametki, Tome 66 (1999) no. 2, pp. 231-241.

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G. A. Omel'yanov; V. V. Trushkov. Dynamics of a~free boundary in a~binary medium with variable thermal conductivity. Matematičeskie zametki, Tome 66 (1999) no. 2, pp. 231-241. http://geodesic.mathdoc.fr/item/MZM_1999_66_2_a10/

[1] Caginalp G., “An analysis of a phase field model of a free boundary”, Arch. Rational Mech. Anal., 92 (1986), 205–245 | DOI | MR | Zbl

[2] Caginalp G., Chen X., “Phase field equations in the singular limit of sharp interface problem”, On the Evolution of Phase Boundaries, IMA Vol. Math. Appl., 43, eds. M. Gurtin, G. B. McFadden, Springer, New York, 1992, 1–28 | MR

[3] Modica L., “The gradient theory of phase translations and the minimal interphase criterion”, Arch. Rational Mech. Anal., 98 (1986), 123–142 | MR

[4] Luckhaus S., Modica L., “The Gibbs–Thomson relation within the gradient theory of phase translations”, Arch. Rational Mech. Anal., 107 (1989), 71–83 | DOI | MR | Zbl

[5] Luckhaus S., “Solutions of the two-phase Stefan problem with the Gibbs–Thomson law for the melting temperature”, European J. Appl. Math., 1 (1990), 101–111 | MR | Zbl

[6] Plotnikov P. I., Starovoitov V. N., “Zadacha Stefana kak predel sistemy fazovogo polya”, Differents. uravneniya, 29:3 (1993), 461–471 | MR | Zbl

[7] Soner H. M., “Convergence of the phase field equations to the Mullins–Sekerka problem with kinetic undercooling”, Arch. Rational Mech. Anal., 131 (1995), 139–197 | DOI | MR | Zbl

[8] Caginalp G., “Stefan and Hele–Shaw type models as asymptotic limits of the phase field equations”, Phys. Rev. A, 39 (1990), 101–111 | MR

[9] Caginalp G., Chen X., “Convergence of the phase field model to its sharp interphase limits”, European J. Appl. Math., 9:4 (1998), 417–445 | DOI | MR | Zbl

[10] Alikakos N., Bates P., “On the singular limit in a phase field model of a phase translations”, Ann. Inst. H. Poincaré. Phys. Théor., 5 (1988), 1–38 | MR

[11] Carr J., Pego R. L., “Metastable patterns in solutions of $u_t=\varepsilon ^2u_{xx}-f(u)$”, Comm. Pure Appl. Math., 42 (1989), 523–576 | DOI | MR | Zbl

[12] Chen X., Elliott C. M., “Asymptotics for a parabolic double obstacle problem”, Proc. Roy. Soc. London. Ser. A, 444 (1994), 429–445 | DOI | MR | Zbl

[13] Nochetto R., Verdi C., “Convergence of double obstacle problem to the generalized geometric motion of fronts”, SIAM J. Math. Anal., 26:4 (1995), 1514–1526 | DOI | MR | Zbl

[14] Danilov V. G., Omelyanov G. A., Radkevich E. V., “Asimptotika resheniya sistemy fazovogo polya i modifitsirovannaya zadacha Stefana”, Differents. uravneniya, 31:3 (1995), 483–491 | MR | Zbl

[15] Danilov V. G., Omelyanov G. A., Radkevich E. V., “Obosnovanie asimptotiki resheniya sistemy fazovogo polya i modifitsirovannaya zadacha Stefana”, Matem. sb., 186:12 (1995), 63–80 | MR | Zbl

[16] Omelyanov G. A., Trushkov V. V., “Geometricheskaya popravka v zadache o dvizhenii svobodnoi granitsy”, Matem. zametki, 63:1 (1998), 151–153 | MR | Zbl

[17] Maslov V. P., Omelyanov G. A., “Asimptoticheskie solitonoobraznye resheniya uravnenii s maloi dispersiei”, UMN, 36:3 (1981), 63–126 | MR | Zbl

[18] Maslov V. P., Danilov V. G., Volosov K. A., Matematicheskoe modelirovanie protsessov teplomassoperenosa, Nauka, M., 1987