Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some local questions for hyperbolic systems with non-regular time
  dependent coefficients   In this note we investigate local properties for microlocally symmetrizable
hyperbolic systems with just time dependent coefficients. Thanks to
Paley-Wiener theorem, we establish finite propagation speed by showing precise
estimates on the evolution of the support of the solution in terms of suitable
norms of the coefficients of the operator and of the symmetrizer. From this
result, local existence and uniqueness follow by quite standard methods. Our
argument relies on the use of Fourier transform, and it cannot be extended to
operators whose coefficients depend also on the space variables. On the other
hand, it works under very mild regularity assumptions on the coefficients of
the operator and of the symmetrizer.

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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol