A question on the Cauchy problem in the Gevrey classes for weakly hyperbolic equations

Tatsuo Nishitani

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arXiv · 2210.02605

A question on the Cauchy problem in the Gevrey classes for weakly hyperbolic equations

Tatsuo Nishitani

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Abstract

For a homogeneous polynomial $p$ in $\xi\in {\bf R}^n$ with Gevrey coefficients, it is known that the Cauchy problem for any realization of $p$ is well-posed in the Gevrey class of order $s<2$ if the characteristic roots are real. In this note, we give examples showing the situation of the converse direction, in particular the optimality of the Gevrey order $s=2$.

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Tatsuo Nishitani. 2022-10-05. A question on the Cauchy problem in the Gevrey classes for weakly hyperbolic equations. https://arxiv.org/abs/2210.02605

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