Geodesic
A Periodic Problem for the Landau–Ginzburg Equation
Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 227-235 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider a periodic problem for the n-dimensional complex Landau–Ginzburg equation. It is shown that in the case of small initial data there exists a unique classical solution of this problem, and an asymptotics of this solution uniform in the space variable is given. The leading term of the asymptotics is exponentially decreasing in time. 
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M. V. Komarov; I. A. Shishmarev. A Periodic Problem for the Landau–Ginzburg Equation. Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 227-235. http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a6/

[1] Ginzburg V. L., Landau L. D., “K teorii sverkhprovodimosti”, ZhETF, 20:12 (1950), 1064–1082

[2] Newell A. C., Whitehead J. A., “Finite bandwidth, finite amplitude convection”, J. Fluid Mech., 38:2 (1969), 279–303 | DOI | Zbl

[3] Kuramoto Y., Yamada T., “Turbulent state in chemical reactions”, Progress Theor. Phys., 56:2 (1976), 679–681 | DOI | MR

[4] Shishmarev I. A., Tsutsumi M., “Asimptotika pri bolshikh vremenakh reshenii kompleksnogo uravneniya Landau–Ginzburga”, Matem. sb., 190:4 (1995), 95–114 | MR

[5] Zhizhiashvili L. V., O sopryazhennykh funktsiyakh i trigonometricheskikh ryadakh, Diss. ... k. f.-m. n., MGU, M., 1967

[6] Naumkin P. I., Shishmarev I. A., Nonlinear Nonlocal Equations in the Theory of Waves, Amer. Math. Soc., Providence (R.I.), 1994 | Zbl