English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the convergence, in the small mass limit, of the stationarysolutions of a class of stochastic damped wave equations, where the frictioncoefficient depends on the state and the noisy perturbation if ofmultiplicative type. We show that the Smoluchowski-Kramers approximation thathas been previously shown to be true in any fixed time interval, is still validin the long time regime. Namely we prove that the first marginals of anysequence of stationary solutions for the damped wave equation converge to theunique invariant measure of the limiting stochastic quasilinear parabolicequation. The convergence is proved with respect to the Wasserstein distanceassociated with the $H^{-1}$ norm.

On the small-mass limit for stationary solutions of stochastic wave equations with state dependent friction