Pseudospectra of semiclassical (pseudo-) differential operators
Författare
Summary, in English
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.
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.
Avdelning/ar
- Matematik (naturvetenskapliga fakulteten)
- Partial differential equations
Publiceringsår
2004
Språk
Engelska
Sidor
384-415
Publikation/Tidskrift/Serie
Communications on Pure and Applied Mathematics
Volym
57
Issue
3
Dokumenttyp
Artikel i tidskrift
Förlag
John Wiley & Sons Inc.
Ämne
- Mathematics
Nyckelord
- principal type
- non-selfadjoint operators
- semiclassical operators
- pseudospectrum
Status
Published
Forskningsgrupp
- Partial differential equations
ISBN/ISSN/Övrigt
- ISSN: 0010-3640