On C ∞ well-posedness of hyperbolic systems with multiplicities

Garetto, Claudia; Ruzhansky, Michael

10.1007%2Fs10231-017-0639-2.pdf (488.35 kB)

On C ∞ well-posedness of hyperbolic systems with multiplicities

journal contribution

posted on 14.01.2016, 15:04 authored by Claudia Garetto, Michael Ruzhansky

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.

Funding

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

History

School

Science

Department

Mathematical Sciences

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.

Publisher

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VoR (Version of Record)

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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

2017

Notes

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.