Galkowski, J;
(2012)
Nonlinear Instability in a Semiclassical Problem.
Communications in Mathematical Physics
, 316
(3)
pp. 705-722.
10.1007/s00220-012-1598-5.
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Abstract
We consider a nonlinear evolution problem with an asymptotic parameter and construct examples in which the linearized operator has spectrum uniformly bounded away from Rez≥0 (that is, the problem is spectrally stable), yet the nonlinear evolution blows up in short times for arbitrarily small initial data. We interpret the results in terms of semiclassical pseudospectrum of the linearized operator: despite having the spectrum in Rez<−γ0<0 , the resolvent of the linearized operator grows very quickly in parts of the region Rez>0 . We also illustrate the results numerically.
| Type: | Article |
|---|---|
| Title: | Nonlinear Instability in a Semiclassical Problem |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00220-012-1598-5 |
| Publisher version: | https://doi.org/10.1007/s00220-012-1598-5 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Initial Data, Half Plane, Nonlinear Evolution, Complex Energy, Nonlinear Instability |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10083918 |
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