19-33 Stephane MALEK

On a partial q-analog of a singularly perturbed problem with Fuchsian and irregular time singularities (625K, pdf) May 2, 19

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Abstract. A family of linear singularly perturbed q-difference differential equations is examined. These equations stand for a q-analog of singularly perturbed PDEs with irregular and Fuchsian singularities in the complex domain recently investigated by A. Lastra and the author. A finite set of sectorial holomorphic solutions is constructed by means of an enhanced version of a classical multisummability procedure due to W. Balser. These functions share a common asymptotic expansion in the perturbation parameter which is shown to carry a double scale structure which pairs q-Gevrey and Gevrey bounds.

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