On $C^\infty$ well-posedness of hyperbolic systems with multiplicities

Claudia Garetto; Michael Ruzhansky

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arXiv · 1512.06243

On $C^\infty$ well-posedness of hyperbolic systems with multiplicities

Claudia Garetto·Michael Ruzhansky

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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 $C^{\infty}$ and in $\mathcal{D}'$. We prove that the analyticity of the coefficients combined with suitable hypotheses on the eigenvalues guarantee the $C^\infty$ 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 \cite{JT} and by the authors in \cite{GR:13}.

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Claudia Garetto, Michael Ruzhansky. 2015-12-19. On $C^\infty$ well-posedness of hyperbolic systems with multiplicities. https://arxiv.org/abs/1512.06243

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