Article ID Journal Published Year Pages File Type
4616504 Journal of Mathematical Analysis and Applications 2013 18 Pages PDF
Abstract

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

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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