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Pseudospectra of semiclassical (pseudo-) differential operators

Dencker, Nils LU ; Sjostrand, J and Zworski, M (2004) In Communications on Pure and Applied Mathematics 57(3). p.384-415
Abstract
The pseudo-spectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. For example, in computational fluid dynamics it affects the study of the stability of laminar flows. In fact, even for the most basic flows, the computations entirely fails to predict what is observed in the experiments.



The explanation is that for non-normal operators the resolvent could be very large far away from the spectrum, which makes computation of the eigenvalues impossible. The occurence of ``false eigenvalues'' is due to the existence of quasi-modes, i.e., approximate local solutions

to the eigenvalue problem. The quasi-modes appear since the Nirenberg-Treves condition (Psi)... (More)
The pseudo-spectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. For example, in computational fluid dynamics it affects the study of the stability of laminar flows. In fact, even for the most basic flows, the computations entirely fails to predict what is observed in the experiments.



The explanation is that for non-normal operators the resolvent could be very large far away from the spectrum, which makes computation of the eigenvalues impossible. The occurence of ``false eigenvalues'' is due to the existence of quasi-modes, i.e., approximate local solutions

to the eigenvalue problem. The quasi-modes appear since the Nirenberg-Treves condition (Psi) is not satisfied for topological reasons. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
principal type, non-selfadjoint operators, semiclassical operators, pseudospectrum
in
Communications on Pure and Applied Mathematics
volume
57
issue
3
pages
384 - 415
publisher
John Wiley & Sons
external identifiers
  • wos:000188201100004
  • scopus:1842832252
ISSN
0010-3640
DOI
10.1002/cpa.20004
language
English
LU publication?
yes
id
07a0b55a-4c44-4f4c-8879-70a525148f2e (old id 289796)
date added to LUP
2007-10-23 11:01:39
date last changed
2017-10-22 04:35:01
@article{07a0b55a-4c44-4f4c-8879-70a525148f2e,
  abstract     = {The pseudo-spectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. For example, in computational fluid dynamics it affects the study of the stability of laminar flows. In fact, even for the most basic flows, the computations entirely fails to predict what is observed in the experiments.<br/><br>
<br/><br>
The explanation is that for non-normal operators the resolvent could be very large far away from the spectrum, which makes computation of the eigenvalues impossible. The occurence of ``false eigenvalues'' is due to the existence of quasi-modes, i.e., approximate local solutions<br/><br>
to the eigenvalue problem. The quasi-modes appear since the Nirenberg-Treves condition (Psi) is not satisfied for topological reasons.},
  author       = {Dencker, Nils and Sjostrand, J and Zworski, M},
  issn         = {0010-3640},
  keyword      = {principal type,non-selfadjoint operators,semiclassical operators,pseudospectrum},
  language     = {eng},
  number       = {3},
  pages        = {384--415},
  publisher    = {John Wiley & Sons},
  series       = {Communications on Pure and Applied Mathematics},
  title        = {Pseudospectra of semiclassical (pseudo-) differential operators},
  url          = {http://dx.doi.org/10.1002/cpa.20004},
  volume       = {57},
  year         = {2004},
}