Analytic and summable solutions of inhomogeneous moment partial differential equations

Abstract

We study the Cauchy problem for a general inhomogeneous linear moment partial differential equation of two complex variables with constant coefficients, where the inhomogeneity is given by the formal power series. We state sufficient conditions for the convergence, analytic continuation and summability of formal power series solutions in terms of properties of the inhomogeneity. We consider both the summability in one variable t (with coefficients belonging to some Banach space of Gevrey series with respect to the second variable z) and the summability in two variables (t,z).

26 pages. arXiv admin note: substantial text overlap with arXiv:1303.1555

References in corpus (1)

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

Cited by in corpus (7)

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• Summability of formal solutions for a family of generalized moment integro-differential equations
• Gevrey estimates for certain moment partial differential equations
• Summable solutions of the Goursat problem for some partial differential equations with constant coefficients
• On the summability and convergence of formal solutions of linear $q$-difference-differential equations with constant coefficients