Formally Well-Posed Cauchy Problems for Linear Partial Differential Equations with Constant Coefficients

In this article we review and extend results on summability of formal solutions of Cauchy problems for linear partial differential equations, in two variables, with constant coefficients. Moreover, we show how one can use these results to find corresponding ones for solutions to inhomogeneous equations, where the inhomogeneity is a formal power series in two variables. We also include an easy example of a PDE where multisummability is required in order to sum the formal solution