On C ∞ well-posedness of hyperbolic systems with multiplicities

Garetto, Claudia; Ruzhansky, Michael

On C ∞ well-posedness of hyperbolic systems with multiplicities

journal contribution

posted on 2016-01-14, 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

Version

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

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.