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Daily Overview |
| Session | |
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Sto1: Stochastic analysis and differential equations Location: L602 Session Chair: Alexandra Blessing | |
| Presentation 1 | |
On the approximation of finite-time Lyapunov exponents for the stochastic Burgers equation 1: Universität Augsburg, Germany; 2: Universität Konstanz, Germany We analyze stochastic partial differential equations (SPDEs) with quadratic nonlinearities close to a change of stability. To this aim we compute finite-time Lyapunov exponents (FTLEs), observing a change of sign based on the interplay between the distance towards the bifurcation and the noise intensity. Our approach relies on a reduction of the infinite-dimensional dynamics to a finite-dimensional stochastic differential equation describing the dominant modes. This allows to carry over results for FTLE from the finite to the infinite dimensional setting. A technical challenge is to provide a suitable control of the nonlinear terms coupling the dominant and stable modes of the SPDE and of the corresponding linearization. We illustrate the theory by applying it to the stochastic Burgers equation | |



