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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
##### Keywords:
Sylvester systems; Gevrey solutions
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