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

In this paper we consider a compact Riemannian manifold (M, g) of class C 1$\cap$ W 2,$\infty$ and the damped wave or Schr\"odinger equations on M , underthe action of a damping function a = a(x). We establish the following fact: ifthe measure of the set {x $\in$ M ; a(x) = 0} is strictly positive, then thedecay in time of the associated energy is at least logarithmic.

A remark on the logarithmic decay of the damped wave and Schr\"odinger equations on a compact Riemannian manifold