arXiv subjects

B. Gess

Publications and source records attributed to B. Gess.

2 recordsLinked to original sources

arXiv2022

Lyapunov exponents and synchronisation by noise for systems of SPDEs

Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the invariant measure, with careful control on the resulting error terms. As a consequence of these estimates, synchronisation by noise is deduced for systems of stochastic reaction-diffusion equations for the first time.

math.PR↗

arXiv2010

The global random attractor for a class of stochastic porous media equations

We prove new $L^2$-estimates and regularity results for generalized porous media equations "shifted by" a function-valued Wiener path. To include Wiener paths with merely first spatial (weak) derivates we introduce the notion of "$ζ$-monotonicity" for the non-linear function in the equation. As a consequence we prove that stochastic porous media equations have global random attractors. In addition, we show that (in particular for the classical stochastic porous media equation) this attractor consists of a random point.

math.PR↗