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Article Dans Une Revue Stochastics and Partial Differential Equations: Analysis and Computations Année : 2017

Generalized regularized long wave equation with white noise dispersion

Résumé

In this article, we address the generalized BBM equation with white noise dispersion which reads du - du(xx) + ux o dW + u(p)u(x)dt = 0, in the Stratonovich formulation, where W(t) is a standard real valued Brownian motion. We first investigate the well-posedness of the initial value problem for this equation. We then prove theoretically and numerically that for a deterministic initial data, the expectation of the norm of the solutions decays to zero at as t approaches to , by assuming that and that the initial data is small in . This decay rate matches the one for solutions of the linear equation with white noise dispersion.
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Dates et versions

hal-03621776 , version 1 (28-03-2022)

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M. Chen, Olivier Goubet, Youcef Mammeri. Generalized regularized long wave equation with white noise dispersion. Stochastics and Partial Differential Equations: Analysis and Computations, 2017, 5 (3), pp.319-342. ⟨10.1007/s40072-016-0089-7⟩. ⟨hal-03621776⟩
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