On C ∞ well-posedness of hyperbolic systems with multiplicities
journal contributionposted 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.
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
- Mathematical Sciences
CitationGARETTO, 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.
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