The damped wave equation with singular damping

Pedro Freitas, Nicolas Hefti, Petr Siegl

Research output: Contribution to journalArticlepeer-review


We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form α/x, α > 0. We establish the exponential stability of the semigroup for all positive α, and determine conditions for the spectrum to consist of a finite number of eigenvalues. As a consequence, we fully characterize the set of initial conditions for which there is extinction of solutions in finite time. Finally, we propose two open problems related to extremal decay rates of solutions.

Original languageEnglish
Pages (from-to)4273-4284
Number of pages12
JournalProceedings of the American Mathematical Society
Issue number10
Publication statusPublished - Oct 2020
Externally publishedYes


  • damped wave equation
  • singular damping
  • empty spectrum
  • finite-time extinction
  • Laguerre polynomials

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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