On Borel summable solutions of the multidimensional heat equation
Volume 105 / 2012
Annales Polonici Mathematici 105 (2012), 167-177
MSC: 35K05, 35C10.
DOI: 10.4064/ap105-2-5
Abstract
We give a new characterisation of Borel summability of formal power series solutions to the $n$-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.
