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Well-posedness of hyperbolic systems with multiplicities and smooth coefficients
journal contribution
posted on 2016-06-09, 12:45 authored by Claudia Garetto, Christian JaehWe study hyperbolic systems with multiplicities and smooth coefficients. In the case of non-analytic, smooth coefficients, we prove well-posedness in any Gevrey class and when the coefficients are analytic, we prove C∞C∞ well-posedness. The proof is based on a transformation to block Sylvester form introduced by D’Ancona and Spagnolo (Boll UMI 8(1B):169–185, 1998) which increases the system size but does not change the eigenvalues. This reduction introduces lower order terms for which appropriate Levi-type conditions are found. These translate then into conditions on the original coefficient matrix. This paper can be considered as a generalisation of Garetto and Ruzhansky (Math Ann 357(2):401–440, 2013), where weakly hyperbolic higher order equations with lower order terms were considered.
Funding
Claudia Garetto partially supported by EPSRC Grant EP/L026422/1. Christian Jäh supported by EPSRC Grant EP/L026422/1.
History
School
- Science
Department
- Mathematical Sciences
Published in
Mathematische AnnalenVolume
369Issue
1-2Pages
441 - 485Citation
GARETTO, C. and JAH, C., 2016. Well-posedness of hyperbolic systems with multiplicities and smooth coefficients. Mathematische Annalen, 369 (1-2), pp. 441–485.Publisher
© The Author(s) 2016. This article is published with open access at Springerlink.comVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/Publication date
2016-06-22Notes
This article is published with open access at Springerlink.com This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.ISSN
0025-5831eISSN
1432-1807Publisher version
Language
- en