## A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations.(English)Zbl 0778.76100

Summary: Small perturbations of an 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 $$div(A_ 1\bigtriangledown u)+A_ 2u=0$$, where $$A_ 1$$ may have singularities in the domain $$U$$ of definition. We study the case when $$U$$ is a half-plane and $$u$$ possesses high Fourier components, analyzing the changes brought about by the singularity $$A_ 1=\infty$$. We show that absorption 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 $$U$$.

### MSC:

 76W05 Magnetohydrodynamics and electrohydrodynamics 35Q60 PDEs in connection with optics and electromagnetic theory 34E05 Asymptotic expansions of solutions to ordinary differential equations
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### References:

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