On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations (Q816465)

Cauchy problems for equations of non-Kovalevski type are under consideration. The author gives a relationship between the classical solution and the Borel sum of the divergent solution for Cauchy data assumed to be holomorphic in a neighbourhood of the origin. It is shown that the classical solution is derived from a deformation of paths in the integral representation of the Borel sum under some conditions for the Cauchy data.