Pseudospectra of the damped wave equation with unbounded damping

Ahmet Arifoski, Petr Siegl

Research output: Contribution to journalArticlepeer-review


We analyze pseudospectra of the generator of the damped wave equation with unbounded damping. We show that the resolvent norm diverges as Re z →-∞. The highly nonnormal character of the operator is a robust effect preserved even when a strong potential is added. Consequently, spectral instabilities and other related pseudospectral effects are present.

Original languageEnglish
Pages (from-to)1343-1362
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Issue number2
Publication statusPublished - 2020
Externally publishedYes


  • Damped wave equation
  • Pseudospectrum
  • Unbounded damping

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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