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 study the strong stabilization of wave equations on some sphere-likemanifolds, with rough damping terms which do not satisfy the geometric controlcondition posed by Rauch-Taylor and Bardos-Lebeau-Rauch. We begin with anunpublished result of G. Lebeau, which states that on S^d , the indicatorfunction of the upper hemisphere strongly stabilizes the damped wave equation,even though the equators, which are geodesics contained in the boundary of theupper hemisphere, do not enter the damping region. Then we extend this resulton dimension 2, to Zoll surfaces of revolution, whose geometry is similar tothat of S^2 . In particular, geometric objects such as the equator, and thehemi-surfaces are well defined. Our result states that the indicator functionof the upper hemi-surface strongly stabilizes the damped wave equation, eventhough the equator, as a geodesic, does not enter the upper hemi-surfaceeither.

Stabilization of Damped Waves on Spheres and Zoll Surfaces of Revolution