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Title: Well-posedness of hyperbolic systems with multiplicities and smooth coefficients
Authors: Garetto, Claudia
Jaeh, Christian
Issue Date: 2016
Publisher: © The Author(s) 2016. This article is published with open access at Springerlink.com
Citation: GARETTO, C. and JAH, C., 2016. Well-posedness of hyperbolic systems with multiplicities and smooth coefficients. Mathematische Annalen, doi:10.1007/s00208-016-1436-8
Abstract: We 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.
Description: 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.
Sponsor: Claudia Garetto partially supported by EPSRC Grant EP/L026422/1. Christian Jäh supported by EPSRC Grant EP/L026422/1.
Version: Published
DOI: 10.1007/s00208-016-1436-8
URI: https://dspace.lboro.ac.uk/2134/21557
Publisher Link: https://doi.org/10.1007/s00208-016-1436-8
Appears in Collections:Published Articles (Maths)

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