17-30 Thomas Dreyfus, Alberto Lastra, Stephane Malek

Twofold q-Gevrey asymptotics for linear singularly perturbed q-difference-differential equations with polynomial coefficients (734K, pdf) Mar 30, 17

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Abstract. We construct analytic and formal solutions for a family of q-difference-differential problems, under the action of a perturbation parameter. This work is a continuation of a prior study focusing on a singularly perturbed q-difference-differential problem for which a phenomenon of multilevel q-Gevrey asymptotics has been observed, owing to the fact that the main equation is factorized as a product of two simpler equations in so-called normal forms, each producing one single level of q-Gevrey asymptotics. The problem under study in this paper is a priori not factorizable. We follow instead a direct approach developed in a work of the first author based on successive applications of two q-Borel-Laplace transforms of different orders both to the same initial problem and which can be described by means of a Newton polygon.

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