From resolvent estimates to damped waves

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

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)143-162
Number of pages20
JournalJournal d'Analyse Mathematique
Volume122
Issue number1
DOIs
StatePublished - Apr 2014

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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