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We study the Cauchy problem for a general homogeneous linear partialdifferential equation in two complex variables with constant coefficients andwith divergent initial data. We state necessary and sufficient conditions forthe summability of formal power series solutions in terms of properties ofdivergent Cauchy data. We consider both the summability in one variable t (withcoefficients belonging to some Banach space of Gevrey series with respect tothe second variable z) and the summability in two variables (t,z). The resultsare presented in the general framework of moment-PDEs.

Summability of formal solutions of linear partial differential equations with divergent initial data