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Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients

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Abstract

We investigate Gevrey order and summability properties of formal power series solutions of some classes of inhomogeneous linear partial differential equations with variable coefficients and analytic initial conditions. In particular, we give necessary and sufficient conditions under which these solutions are convergent or are k-summable, for a convenient k, in a given direction.

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Notes

  1. We denote \(\widetilde {q}\) with a tilde to emphasize the possible divergence of the series \(\widetilde {q}\).

  2. A subsector Σ of a sector \({\Sigma }^{\prime }\) is said to be a proper subsector and one denotes \({\Sigma }\Subset {\Sigma }^{\prime }\) if its closure in \(\mathbb {C} \) is contained in \({\Sigma }^{\prime }\cup \{0\}\).

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  1. Lycée Les Pierres Vives, 1 rue des Alouettes, F-78 420, Carrières-sur-Seine, France

    Pascal Remy

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  1. Pascal Remy
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Correspondence to Pascal Remy.

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Remy, P. Gevrey Order and Summability of Formal Series Solutions of some Classes of Inhomogeneous Linear Partial Differential Equations with Variable Coefficients. J Dyn Control Syst 22, 693–711 (2016). https://doi.org/10.1007/s10883-015-9301-8

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  • DOI: https://doi.org/10.1007/s10883-015-9301-8

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