Geodesic
A Periodic Problem for the Landau--Ginzburg Equation
Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 227-235.

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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/

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