M. Núñez y J. Rojo
A WKB analysis of the Alfvén spectrum of the linearized Magnetohydrodynamics equations
Appl. Math., 38 (1993), pp. 23-38

Small perturbations of a equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation ${\rm div} (A_1\,\nabla u)+A_2\, u=0$, where $\alpha _1$ may have singularities in the domain $U$ of definition. We study the case where $U$ is a half-plane and $u$ possesses high Fourier components, analyzing the changes brought about by the singularity $A_1=\infty $. We show that absortion of energy takes place precisely at this singularity, that the solutions have a near harmonic
character and the integrability characteristics of the boundary data are kept throughout~$U$.
AMS(MOS) subject classification: 76W05, 34E05

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