Details

Autor(en) / Beteiligte

• Christianson, Hans
• Schenck, Emmanuel
• Vasy, András
• Wunsch, Jared

Titel

From resolvent estimates to damped waves

Ist Teil von

• Journal d'analyse mathématique (Jerusalem), 2014-04, Vol.122 (1), p.143-162

Ort / Verlag

Heidelberg: The Hebrew University Magnes Press

Erscheinungsjahr

2014

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the undamped set. We show that if replacing the damping term with a higher-order complex absorbing potential gives an operator enjoying polynomial resolvent bounds on the real axis, then the “resolvent” associated to our damped problem enjoys bounds of the same order. It is known that the necessary estimates with complex absorbing potential can also be obtained via gluing from estimates for corresponding non-compact models.