Pseudospectra of semiclassical (pseudo-) differential operators
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/289796
- author
- Dencker, Nils LU ; Sjostrand, J and Zworski, M
- organization
- publishing date
- 2004
- 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 Inc.
- 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
- 2016-04-01 15:55:29
- date last changed
- 2022-04-07 01:39:16
@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}},
keywords = {{principal type; non-selfadjoint operators; semiclassical operators; pseudospectrum}},
language = {{eng}},
number = {{3}},
pages = {{384--415}},
publisher = {{John Wiley & Sons Inc.}},
series = {{Communications on Pure and Applied Mathematics}},
title = {{Pseudospectra of semiclassical (pseudo-) differential operators}},
url = {{http://dx.doi.org/10.1002/cpa.20004}},
doi = {{10.1002/cpa.20004}},
volume = {{57}},
year = {{2004}},
}