A. A. Agrachev, S. A. Vakhrameev, “Chronological series and the Cauchy–Kovalevskaya theorem”, Journal of Soviet Mathematics, 1983, 21:2, 231–250
We consider the Cauchy problem for a system of partial differential equations. We prove an existence theorem for a solution of this problem which is analytic in the spatial variable under the assumption of measurability and local integrability of the right side with respect to time only. The solution is represented in the form of a chronological series.