@article{3872fae3b7684487bf8ac0034701e8ba,
title = "Pseudospectra of the damped wave equation with unbounded damping",
abstract = "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.",
keywords = "Damped wave equation, Pseudospectrum, Unbounded damping",
author = "Ahmet Arifoski and Petr Siegl",
note = "Funding Information: \ast Received by the editors October 18, 2018; accepted for publication (in revised form) January 21, 2020; published electronically March 24, 2020. https://doi.org/10.1137/18M1221400 Funding: The research of the second author and in particular work on this paper was supported by the Swiss National Science Foundation Ambizione under grant PZ00P2 154786 (until December 2017) and by FCT (Portugal) project PTDC/MAT-CAL/4334/2014. \dagger Kantonsschule Olten, 4600 Olten, Switzerland (ahmet.arifoski@kantiolten.ch). \ddagger School of Mathematics and Physics, Queen's University Belfast, Belfast, BT7 1NN, UK (p.siegl@ qub.ac.uk). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2020",
doi = "10.1137/18M1221400",
language = "English",
volume = "52",
pages = "1343--1362",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}