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Hyperbolic boundary value problems for symmetric systems with variable multiplicities. (English) Zbl 1073.35155

The authors analyse stability of the hyperbolic initial-boundary-value and shock problems to a class of systems with characteristics of variable multiplicity, for which Majda’s block structure condition does not hold. The authors extend the construction of Kreiss symmetrizers to the case of such systems and apply this new tool to the problem of nonlinear stability of shock waves in magnetohydrodynamics. Possible extensions to the viscous case are also discussed.

MSC:

35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
35B35 Stability in context of PDEs
76L05 Shock waves and blast waves in fluid mechanics
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
35L50 Initial-boundary value problems for first-order hyperbolic systems
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