The propagation of analyticity for sufficiently smooth solutions to either strictly hyperbolic, or smoothly symmetrizable nonlinear systems, dates back to Lax (Comm. on Pure Appl. Math. 1953) and Alinhac and Métivier (Invent. Math. 1984). Here we consider the general case of a system with real, possibly multiple, characteristics, and we ask which regularity should be a priori required of a given solution in order that it enjoys the propagation of analyticity. By using the technique of the quasi-symmetrizer of a hyperbolic matrix, we prove, in the one-dimensional case, the propagation of analyticity for those solutions which are Gevrey functions of order s for some s < m/(m − 1), m being the maximum multiplicity of the characteristics.
Analitic propagation for nonlinear weakly hyperbolic systems
TAGLIALATELA, Giovanni
2010-01-01
Abstract
The propagation of analyticity for sufficiently smooth solutions to either strictly hyperbolic, or smoothly symmetrizable nonlinear systems, dates back to Lax (Comm. on Pure Appl. Math. 1953) and Alinhac and Métivier (Invent. Math. 1984). Here we consider the general case of a system with real, possibly multiple, characteristics, and we ask which regularity should be a priori required of a given solution in order that it enjoys the propagation of analyticity. By using the technique of the quasi-symmetrizer of a hyperbolic matrix, we prove, in the one-dimensional case, the propagation of analyticity for those solutions which are Gevrey functions of order s for some s < m/(m − 1), m being the maximum multiplicity of the characteristics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
