Borel summability for a formal solution of $\frac{\partial}{\partial t}u(t,x)= \bigl(\frac{\partial}{\partial x}\bigr)^2u(t,x) +t\bigl(t\,\frac{\partial}{\partial t}\bigr)^3u(t,x)$
Volume 97 / 2012
Banach Center Publications 97 (2012), 161-168
MSC: Primary 34M30; Secondary 34M25.
DOI: 10.4064/bc97-0-12
Abstract
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 $\phi(x)$ is an entire function of exponential order at most $2$.
