Pseudospectra of semiclassical (pseudo-) differential operators

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

principal type

non-selfadjoint operators

semiclassical operators

pseudospectrum

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)