Abstract
We prove that the Cauchy problem for a hyperbolic, homogeneous equation with \(\mathcal{C}^{\infty}\) coefficients depending on time, is well posed in every Gevrey class, although in general it is not well-posed in \(\mathcal{C}^{\infty}\) provided the characteristic roots satisfy the condition
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Kinoshita, T., Spagnolo, S. Hyperbolic Equations with Non-analytic Coefficients. Math. Ann. 336, 551–569 (2006). https://doi.org/10.1007/s00208-006-0009-7
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DOI: https://doi.org/10.1007/s00208-006-0009-7