On C^∞ well-posedness of hyperbolic systems with multiplicities

2015/12/19 by Claudia Garetto, Michael Ruzhansky, Garetto, Claudia +1
Mathematics · Physics and Astronomy · #35L40 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 35L25 #Quantum chaos and dynamical systems #Secondary 46F05

paper · pdf · doi:10.48550/arxiv.1512.06243

openalex publication_date 2015/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study first order hyperbolic systems 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^∞ and in D'. We prove that the analyticity of the coefficients combined with suitable hypotheses on the eigenvalues guarantee the C^∞ well-posedness of the corresponding Cauchy problem. This result is an extension to systems of the analogous results for scalar equations recently obtained by Jannelli and Taglialatela in \citeJT and by the authors in \citeGR:13.

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