In this paper we study the Borel summability of a certain divergent formal power series solution for an initial value problem. We show the Borel summability under the condition that an initial value function ϕ(x) is an entire function of exponential order at most 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-12,
author = {Hiroshi Yamazawa},
title = {Borel summability for a formal solution of $\partial$/$\partial$t u(t,x) = ($\partial$/$\partial$x)$^2$ u(t,x) + t(t$\partial$/$\partial$t)$^3$ u(t,x)},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {161-168},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-12}
}
Hiroshi Yamazawa. Borel summability for a formal solution of ∂/∂t u(t,x) = (∂/∂x)² u(t,x) + t(t∂/∂t)³ u(t,x). Banach Center Publications, Tome 97 (2012) pp. 161-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc97-0-12/