Approximations of the solution of a stochastic Ginzburg-Landau equation

Brigitte Breckner, Hannelore Lisei


This paper presents a method to approximate the solution of
a stochastic Ginzburg-Landau equation with multiplicative noise term.
Error estimates for the approximation of the solution are given.


stochastic Ginzburg-Landau equation; power-type nonlinearity; multiplicative noise

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Barton-Smith, M., Global solution for a stochastic Ginzburg-Landau equation with multiplicative noise, Stochastic Anal. Appl., 22(2004), no. 1, 1–18.

Barton-Smith, M., Invariant measure for the stochastic Ginzburg Landau equation, NoDEA Nonlinear Differential Equations Appl., 11(2004), no. 1, 29–52.

Cao, G., He, K., On a type of stochastic differential equations driven by countably many Brownian motions, J. Funct. Anal., 203(2003), no. 1, 262–285.

Gajewski, H., ¨Uber N¨aherungsverfahren

zur L¨osung der nichtlinearen Schr¨odinger-Gleichung, Math. Nachr., 85(1978), 283–302.

Hoshino, M., Inahama, Y, Naganuma, N., Stochastic complex Ginzburg-Landau equation with space-time white noise, Electron. J. Probab., 22(2017), Paper No. 104, 68 pp.

Jiu Q., Liu, J., Existence and uniqueness of global solutions of [the nonlinear Schr¨odinger equation] on R2, Acta Math. Appl. Sinica (English Ser.), 13(1997), no. 4, 414–424.

Keller, D., Lisei, H., Variational solution of stochastic Schr¨odinger equations with power-type nonlinearity, Stoch. Anal. Appl., 33(2015), 653–672.

Lions, J.-L., Quelques m´ethodes de r´esolution des probl`emes aux limites non lin´eaires, Dunod, Gauthier-Villars, Paris, 1969.

Lisei, H., Keller, D., A stochastic nonlinear Schr¨odinger problem in variational formulation. NoDEA Nonlinear Differential Equations Appl., 23(2016), no. 2, Art. 22, 27 pp.

Liu, D., Convergence of the spectral method for stochastic Ginzburg–Landau equation driven by space-time white noise, Commun. Math. Sci., 1(2003), no. 2, 361–375.

Liu, X., Jia, H., Existence of suitable weak solutions of complex Ginzburg-Landau equations and properties of the set of singular points, J. Math. Phys., 44(2003), no. 11, 5185–5193.

Pecher H., von Wahl, W., Time dependent nonlinear Schr¨odinger equations, Manuscripta Math., 27(1979), no. 2, 125–157.

Temam, R., Infinite-dimensional dynamical systems in mechanics and physics,

volume 68 of Applied Mathematical Sciences, Springer-Verlag, New York, second edition, 1997.

Vishik, M. J., Fursikov, A. V., Mathematical problems of statistical hydromechanics, Kluwer Academic Publishers Group, Dordrecht, 1988.

Zeidler, E., Nonlinear functional analysis and its applications. II/A: Linear monotone operators, Springer-Verlag, New York, 1990.



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