The authors consider the following Cauchy problem \[ \begin{aligned} \partial_tu- \sum_{|\alpha|\leq m} a_\alpha(t, x)\partial^\alpha_x u&= f(t,x),\\ u|_{t= 0}&= u_0(x),\end{aligned} \] where \(a_\alpha(t,x)\) is an \(N\times N\) matrix of functions in \(C^\infty((T_1, T_2); A(\Omega))\), \(A(\Omega)\) is the set of the real analytic functions in \(\Omega\), \(u\), \(u_0\) and \(f(t,x)\) are \(N\)-dimensional vectors, \(\Omega\) is a bounded domain in \(\mathbb{R}^d\). In this paper the authors give the positive answer to the conjecture of W. Matsumoto and H. Yamahara to obtain the Cauchy-Kowalevskaya theorem of Nagumo type.
For the entire collection see [Zbl 1027.00009].