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The well-posedness issue in Sobolev spaces for hyperbolic systems with Zygmund-type coefficients

Colombini, Ferruccio
•
DEL SANTO, DANIELE
•
Fanelli, Francesco
•
Métivier, Guy
2015
  • journal article

Periodico
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Abstract
In this paper we study the well-posedness of the Cauchy problem for first order hyperbolic systems with constant multiplicities and with low regularity coefficients depending just on the time variable. We consider Zygmund and log-Zygmund type assumptions, and we prove well-posedness in H^infty respectively without loss and with finite loss of derivatives. The key to obtain the results is the construction of a suitable symmetrizer for our system, which allows us to recover energy estimates (with or without loss) for the hyperbolic operator under consideration. This can be achievied, in contrast with the classical case of systems with smooth (say Lipschitz) coefficients, by adding one step in the diagonalization process, and building the symmetrizer up to the second order.
DOI
10.1080/03605302.2015.1082107
WOS
WOS:000364224900004
Archivio
http://hdl.handle.net/11368/2851862
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-84947034300
https://www.tandfonline.com/doi/full/10.1080/03605302.2015.1082107
Diritti
open access
FVG url
https://arts.units.it/request-item?handle=11368/2851862
Soggetti
  • Energy estimate

  • H^infty well-posedne

  • Hyperbolic system wit...

  • Microlocal symmetriza...

  • Zygmund and log-Zygmu...

Scopus© citazioni
7
Data di acquisizione
Jun 14, 2022
Vedi dettagli
Web of Science© citazioni
9
Data di acquisizione
Mar 27, 2024
Visualizzazioni
1
Data di acquisizione
Apr 19, 2024
Vedi dettagli
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