Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables

Abstract

We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given direction. When restricted to the case of constants coefficients, these conditions coincide with those given by D.A. Lutz, M. Miyake, R. Schaefke in a 1999 article, and we thus provide a new proof of their result.