Faierman, M. and Mennicken, R. (2010) THE ESSENTIAL SPECTRUM OF A PERTURBED OPERATOR ARISING IN TWO-DIMENSIONAL MAGNETOHYDRODYNAMICS. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 88 (2). pp. 169-182. ISSN 1446-7887,
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Descloux and Geymonat considered a model problem in two-dimensional magnetohydrodynamics and conjectured that the essential spectrum has an explicitly given band structure. This conjecture was recently proved by Faierman, Mennicken, and Moller by reducing the problem to that for a 2 x 2 block operator matrix. In a subsequent paper Faierman and Mennicken investigated the essential spectrum for the problem arising from a particular type of perturbation of precisely one of the operator entries in the matrix representation cited above of the original problem considered by Descloux and Geymonat. In this paper we extend the results of that work by investigating the essential spectrum for the problem arising from particular types of perturbations of all but one of the aforementioned operators. It remains an open question whether one can perturb the exceptional operator in such a way as to leave the essential spectrum unchanged.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; essential spectrum; perturbed operator; magnetohydrodynamics |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Aug 2020 08:39 |
| Last Modified: | 03 Aug 2020 08:39 |
| URI: | https://pred.uni-regensburg.de/id/eprint/24925 |
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