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Systems of Singular Differential Operators of Mixed Order and Applications to 1 - Dimensional MHD Problems: Systems of Singular Differential Operators of Mixed Order and Applications to 1 - Dimensional MHD Problems by Volker Hardt; Reinhard Mennicken; Serguei Naboko is a Mathematics article available to read on EtoBox.

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In some weighted La vector space we study a symmetric semibounded operator ILb which is given by a 3 x 3 system of ordinary differential operators on an interval1 [O,ro] with a singularity at r = 0 (see (0.1)). This system can be considered as a "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 L of the symmetric operator ILL (and its closure LO) 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 (r1,ro] with 0 < ri < ro. In the corresponding physical model these bands are called Alf%n spectrum and slow magnetosonic spectrum. It is shown that the singularity in 0 generates additional components of the essential spectrum which under specific conditions, a

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Author

Volker Hardt; Reinhard Mennicken; Serguei Naboko

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); Wiley - V C H Verlag GmbbH & Co.; Wiley (ISSN 0025-584X)

Published

1999

Language

EN

Field

Mathematics (Physical Sciences)