METIVIER, Guy; ZUMBRUN, Kevin

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METIVIER, Guy
Institut de Mathématiques de Bordeaux [IMB]

ZUMBRUN, Kevin
Department of Mathematics IU

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Journal of Differential Equations. 2005, vol. 211, p. pp 61--134

Elsevier

Résumé en anglais

We extend the Kreiss–Ma jda theory of stability of hyperbolic initial– boundary-value and shock problems to a class of systems, notably in- cluding the equations of magnetohydrodynamics (MHD), for which Ma jda's block structure condition does not hold: namely, simulta- neously symmetrizable systems with characteristics of variable mul- tiplicity, satisfying at points of variable multiplicity either a “totally nonglancing” or a “nonglancing and linearly splitting” condition. At the same time, we give a simple characterization of the block struc- ture condition as “geometric regularity” of characteristics, defined as analyticity of associated eigenpro jections The totally nonglancing or nonglancing and linearly splitting conditions are generically satisfied in the simplest case of crossings of two characteristics, and likewise for our main physical examples of MHD or Maxwell equations for a crys- tal. Together with previous analyses of spectral stability carried out by Gardner–Kruskal and Blokhin–Trakhinin, this yields immediately a number of new results of nonlinear inviscid stability of shock waves in MHD in the cases of parallel or transverse magnetic field, and recovers the sole previous nonlinear result, obtained by Blokhin–Trakhinin by direct “dissipative integral” methods, of stability in the zero-magnetic field limit.< Réduire

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Hyperbolic Boundary Value Problems for Symmetric Systems with Variable Multiplicities

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