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Quasi-symmetrization of hyperbolic systems and propagation of the analytic regularity. (English) Zbl 0916.35063
The notion of quasi-symmetrization of first-order hyperbolic systems is introduced and applied to Sylvester systems, i.e. systems obtained by reducing a scalar equation of higher order. Then the authors prove that for any semilinear weakly hyperbolic systems of \(N\) equations the Gevrey solutions in \(x\) of order \(s< N/(N-1)\) remain analytic.

MSC:
35L45 Initial value problems for first-order hyperbolic systems
35B65 Smoothness and regularity of solutions to PDEs
35L30 Initial value problems for higher-order hyperbolic equations
35L60 First-order nonlinear hyperbolic equations
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