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

Ferruccio Colombini; Tatsuo Nishitani

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

Analysis of PDEs 2018-06-19 v2

Authors: Ferruccio Colombini , Tatsuo Nishitani

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 $s<s'<1+(n+alpha)/2$ .

Keywords

Cauchy problem second order differential operators Gevrey class well-posedness two independent variables

Cite

@article{arxiv.1712.05253,
  title  = {On the Cauchy problem for $D_t^2-D_x(b(t)a(x))D_x$},
  author = {Ferruccio Colombini and Tatsuo Nishitani},
  journal= {arXiv preprint arXiv:1712.05253},
  year   = {2018}
}

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