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The Ginzburg-Landau equations for superconductivity with random fluctuations. (English) Zbl 1172.35083

Isakov, Victor (ed.), Sobolev spaces in mathematics. III: Applications in mathematical physics. New York, NY: Springer; Novosibirsk: Tamara Rozhkovskaya Publisher (ISBN 978-0-387-85651-3/hbk; 978-5-901873-28-1; 978-0-387-85791-6/set; 978-0-387-85652-0/e-book). International Mathematical Series 10, 25-133 (2009).
The paper is devoted to the study of the boundary value problem of Neumann type for the stochastic Ginzburg-Landau equations with additive and multiplicative white noise. The authors use white noise with minimal restriction on its independence property. The existence and uniqueness of weak and strong statistical solutions are proved. The used approach is based on using difference schemes for the Ginzburg-Landau equation.
The Ginzburg-Landau model is studied in situations for which the described physical processes are subject to uncertainty, due, for example, to thermal fluctuations or material inhomogeneities. An adequate description of such processes is possible with the help of stochastic partial differential equations.
For the entire collection see [Zbl 1152.46001].

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
35Q60 PDEs in connection with optics and electromagnetic theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
82D55 Statistical mechanics of superconductors
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