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Title: On C ∞ well-posedness of hyperbolic systems with multiplicities
Authors: Garetto, Claudia
Ruzhansky, Michael
Issue Date: 2017
Publisher: © The Author(s) 2017. This article is published with open access at Springerlink.com
Citation: GARETTO, C. and RUZHANSKY, M., 2017. On C ∞ well-posedness of hyperbolic systems with multiplicities. Annali di Matematica Pura ed Applicata, 196 (5), pp. 1819–1834.
Abstract: In this paper, we study first-order hyperbolic systems of any order with multiple characteristics (weakly hyperbolic) and time-dependent analytic coefficients. The main question is when the Cauchy problem for such systems is well-posed in C∞C∞ and in D′D′ . We prove that the analyticity of the coefficients combined with suitable hypotheses on the eigenvalues guarantees the C∞C∞ well-posedness of the corresponding Cauchy problem.
Description: 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: The first author was supported by the EPSRC First grant EP/L026422/1. The second author was supported in parts by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02. No new data was collected or generated during the course of this research
Version: Published
DOI: 10.1007/s10231-017-0639-2
URI: https://dspace.lboro.ac.uk/2134/20041
Publisher Link: https://doi.org/10.1007/s10231-017-0639-2
Appears in Collections:Published Articles (Maths)

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