Geodesic
Connected kink states in nonlinear inhomogeneous media
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 1, pp. 115-128 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The equation $\phi_t=\epsilon^2\Delta\phi+H^2(x,y)\sin\phi$ is considered arising in liquid crystal physics. The kink formation and motion are studied. The relaxation times are calculated. It is shown that there are possible connected kink states. Parameters of these states are found for small $\epsilon$. 
@article{TMF_1996_107_1_a9,
     author = {N. M. Bessonov and S. A. Vakulenko},
     title = {Connected kink states in nonlinear inhomogeneous media},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {115--128},
     year = {1996},
     volume = {107},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a9/}
}
TY  - JOUR
AU  - N. M. Bessonov
AU  - S. A. Vakulenko
TI  - Connected kink states in nonlinear inhomogeneous media
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 115
EP  - 128
VL  - 107
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a9/
LA  - ru
ID  - TMF_1996_107_1_a9
ER  - 
%0 Journal Article
%A N. M. Bessonov
%A S. A. Vakulenko
%T Connected kink states in nonlinear inhomogeneous media
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 115-128
%V 107
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a9/
%G ru
%F TMF_1996_107_1_a9
N. M. Bessonov; S. A. Vakulenko. Connected kink states in nonlinear inhomogeneous media. Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 1, pp. 115-128. http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a9/

[1] Allen S., Cahn J., Acta Metallurgica, 27 (1979), 1084 | DOI

[2] Cahn J. W., Hilliard J. H., J. Chem. Phys., 28:2 (1958), 258 | DOI

[3] Owen N. C., Rubinstein J., Sternberg P., Proc. R. Soc. London, A429 (1990), 505 | DOI | MR | Zbl

[4] Sternberg P., Rocky Mountain J. of Math., 21:2 (1991), 799 | DOI | MR | Zbl

[5] Fife P. C., Mathematical aspects of reacting and diffusing systems, Springer, Berlin, 1979 | MR

[6] Khenri D., Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Mir, M., 1985 | MR

[7] Nikolis G., Prigozhin I., Samoorganizatsiya v neravnovesnykh sistemakh, Mir, M., 1977

[8] Molotkov I. A., Vakulenko S. A., Sosredotochennye nelineinye volny, Izd-vo LGU, L., 1988 | MR

[9] Babin A. V., Vishik M. I., Attraktory evolyutsionnykh uravnenii, Nauka, M., 1989 | MR | Zbl

[10] Ladyzhenskaya O. A., UMN, 42:6 (1987), 25 | MR | Zbl

[11] Chueshov I. D., UMN, 48:3 (1993), 135 | MR | Zbl

[12] Volovik G. E., Mineev V. P., Pisma v ZhETF, 23 (1976), 647

[13] Volovik G. E., Mineev V. P., Pisma v ZhETF, 24 (1976), 605

[14] Volosov K. A., Maslov V. P., Danilov V. G., Matematicheskoe modelirovanie protsessov izgotovleniya SBIS, Nauka, M., 1984 | MR

[15] Maslov V. P., Omelyanov G. E., UMN, 36:3 (1981)

[16] Danilov V. G., Matem. zametki, 50:3 (1991), 77 | MR | Zbl

[17] De Mottoni P., Schatzman P., Comptes Rendus Acad. Sci. Paris, Ser. I Math., 309 (1989), 453 | MR | Zbl

[18] Rubinstein J., Keller J., Sternberg P., Siam J. on Appl. Math., 49 (1989), 116 | DOI | MR | Zbl

[19] Kohn R. V., Bronsard L., J. Diff. Eq., 90 (1991), 211 | DOI | MR | Zbl

[20] Brusov P. N., Popov V. N., Sverkhtekuchest i kollektivnye svoistva kvantovykh zhidkostei, Nauka, M., 1988

[21] De Zhen P., Fizika zhidkikh kristallov, Mir, M., 1977

[22] Aero E. L., Bulygin A. N., FTT, 13:6 (1971), 1701

[23] Aero E. L., Optika i spektoroskopiya, 65:2 (1988), 342

[24] Aero E. L., Zakharov A. V., Itogi nauki i tekhniki. Ser. Komplesnye i spetsialnye razdely mekhaniki, 3, no. 2, VINITI, 1988, 163

[25] De Giorgi E., Boll. Un. Mat. Ital., 14A:5 (1977), 213 | Zbl

[26] Modica L., Arch. Rat. Mech. Anal., 98 (1987), 123 | DOI | MR | Zbl

[27] Modica L., Annales Inst. H. Poincare. L'Analyse Nonlinaire, 5 (1987), 453

[28] Jolly M., J. Diff. Equat., 78 (1989), 220 | DOI | MR | Zbl

[29] Babich M. V., Algebra i analiz, 2:3 (1990), 63 | MR

[30] Babich M. V., Algebra i analiz, 3:1 (1991), 57 | MR

[31] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1979 | MR

[32] Fife P. C., Macleod J. B., Arch. Rat. Mech. Anal., 65 (1977), 335 | DOI | MR | Zbl

[33] Cage M., Hamilton R. S., J. Diff. Geom., 23 (1986), 69 | DOI | MR

[34] Fomenko A. T., Variatsionnye problemy v topologii, Nauka, M., 1982 | MR

[35] Fusco G. A., “Geomtric approach to the dynamics of $u_t=\epsilon^2 u+f(u)$”, Lect. Notes in Phys., 359, Springer, Berlin–Heidelberg, 1990, 53–73 | DOI | MR

[36] Carr J., Pego R., “Very slow phase separation in one dimension”, Lect. Notes in Phys., 344, eds. M. Rasele et al., Springer, 1989, 216 | DOI | MR | Zbl

[37] Carr J., Pego R., Comm. Pure and Appl. Math., 42 (1989), 523 | DOI | MR | Zbl