Hardt, Volker and Mennicken, Reinhard and Naboko, Serguei (1999) Systems of singular differential operators of mixed order and applications to 1-dimensional MHD problems. MATHEMATISCHE NACHRICHTEN, 205 (1). pp. 19-68. ISSN 0025-584X
Full text not available from this repository.Abstract
In some weighted L-2 vector space we study a symmetric semibounded operator IL'(0) which is given by a 3 x 3 system of ordinary differential operators on an interval [0, r(0)] with a singularity at r = 0 (see (0.1)). This system can be considered asa "smooth" perturbation of a more specific physical model describing the oscillations of plasma in an equilibrium configuration in a cylindrical domain (see (1.12)). This perturbation is smooth in-the sense that in the system under study in comparison with the physical model only the smooth parts-of:the coefficients are changed conserving all types of singularities. It is the goal of this paper to construct a suitable selfadjoint extension IL of the symmetric operator IL'(0) land its closure IL0) and to determine the essential spectrum of this extension. The essential spectrum consists of two bands (which may overlap) if we exclude the singularities by considering the system on an interval [r(1), r(0)] with 0 < r(1) < r(0). In the corresponding physical model these bands are called Alfven spectrum and slow magnetosonic spectrum. It is shown that the singularity in 0 generates additional components of the essential spectrum which under specific conditions, as in the case of the physical model, "disappear" in the two bands known from the "regular" case [r(1), r(0)] with r(1) SE arrow 0.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPECTRUM; self adjoint operator matrices; systems of singular ordinary differential; operators; essential spectrum; magnetohydrodynamics |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Dec 2022 05:21 |
| Last Modified: | 01 Dec 2022 05:21 |
| URI: | https://pred.uni-regensburg.de/id/eprint/48698 |
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