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arXiv · 1509.01603

On hyperbolic systems with time dependent Hölder characteristics

Claudia Garetto·Michael Ruzhansky
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Abstract

In this paper we study the well-posedness of weakly hyperbolic systems with time dependent coefficients. We assume that the eigenvalues are low regular, in the sense that they are Hölder with respect to $t$. In the past these kind of systems have been investigated by Yuzawa \cite{Yu:05} and Kajitani \cite{KY:06} by employing semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform property of the eigenvalues, we improve the Gevrey well-posedness result of \cite{Yu:05} and we obtain well-posedness in spaces of ultradistributions as well. Our main idea is a reduction of the system to block Sylvester form and then the formulation of suitable energy estimates inspired by the treatment of scalar equations in \cite{GR:11}

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Claudia Garetto, Michael Ruzhansky. 2015-09-18. On hyperbolic systems with time dependent Hölder characteristics. https://arxiv.org/abs/1509.01603

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