On k-summability of formal solutions for certain partial differential operators with polynomial coefficients

Abstract

Abstract. We study the k-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in t. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.

The Stokes Phenomenon for Some Moment Partial Differential Equations

“…Let us recall that the theory of summability of the formal solutions of PDEs has been recently intensively developed by such authors as M. Hibino [4]; K. Ichinobe and M. Miyake [7]; K. Ichinobe [5,6]; A. Lastra, S. Malek and J. Sanz [12]; P. Remy [19], H. Tahara and H. Yamazawa [21]; H. Yamazawa and M. Yoshino [23]; M. Yoshino [24,25]; and others.…”