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arXiv · 1712.05253

On the Cauchy problem for $D_t^2-D_x(b(t)a(x))D_x$

Ferruccio Colombini·Tatsuo Nishitani
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Abstract

We consider the Cauchy problem for second order differential operators with two independent variables $P=D_t^2-D_x(b(t)a(x))D_x$. Assume that $b(t)$ is a nonnegative $C^{n,alpha}$ function and $a(x)$ is a nonnegative Gevrey function of order $s>1$ we prove that the Cauchy problem for $P$ is well-posed in the Gevrey class of any order $s<s'<1+(n+alpha)/2$.

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Ferruccio Colombini, Tatsuo Nishitani. 2017-12-14. On the Cauchy problem for $D_t^2-D_x(b(t)a(x))D_x$. https://arxiv.org/abs/1712.05253

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