Abstract
The technique of quasi-symmetrizer has been applied to the well-posedness of the Cauchy problem for scalar operators [10], [13] and linear systems [5], [15], [4], and to the propagation of analitycity for solutions to semi-linear systems [6]. In all these works, it is assumed that the principal symbol depends only on the time variable.
In this note we illustrate, in some special cases, a new property of the quasisymmetrizer which allows us to generalize the result in [6] to semi-linear systems with coefficients depending also on the space variables [21]. Such a property is closely connected with some interesting inequalities on the eigenvalues of a hyperbolic matrix.
We expect that this technique applies also to other problems.
Keywords: First order hyperbolic systems, Quasi-symmetrizer, Glaeser inequality
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Spagnolo, S., Taglialatela, G. Some algebraic properties of the hyperbolic systems. Ann. Univ. Ferrara 52, 457–470 (2006). https://doi.org/10.1007/s11565-006-0031-4
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DOI: https://doi.org/10.1007/s11565-006-0031-4