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Pseudospectra of semiclassical (pseudo-) differential operators

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Author

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.

Department/s

Publishing year

2004

Language

English

Pages

384-415

Publication/Series

Communications on Pure and Applied Mathematics

Volume

57

Issue

3

Document type

Journal article

Publisher

John Wiley & Sons Inc.

Topic

  • Mathematics

Keywords

  • principal type
  • non-selfadjoint operators
  • semiclassical operators
  • pseudospectrum

Status

Published

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 0010-3640