17.02.2026 11:15 Alexandra Blessing:
Finite-time Lyapunov exponents for stochastic partial differential equations with rough noiseMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)
We analyze the qualitative behavior of stochastic partial differential equations (SPDEs) with a particular focus on bifurcations. To this aim we investigate a change of sign in the finite-time Lyapunov exponents (FTLEs) of the SPDE in a small noise regime and close to a phase transition. Under suitable assumptions, the FTLEs are positive and thus indicate a change of stability. These results are applied to the stochastic Allen-Cahn and Burgers equation with non-Markovian noise and to singular SPDEs. Moreover, we also discuss properties of FTLEs, in particular large deviations type results.