ON THE MULTIPLE-SCALE ANALYSIS FOR SOME LINEAR PARTIAL q-DIFFERENCE AND DIFFERENTIAL EQUATIONS WITH HOLOMORPHIC COEFFICIENTS

International audienceThe analytic and formal solutions of certain family of q-difference-differential equations under the action of a complex perturbation parameter is considered. The previous study [10] provides information in the case when the main equation under study is factoriz-able, as a product of two equations in the so-called normal form. Each of them gives rise to a single level of q-Gevrey asymptotic expansion. In the present work, the main problem under study does not suffer any factorization, and a different approach is followed. More precisely, we lean on the technique developed in [4], where the first author makes distinction among the different q-Gevrey asymptotic levels by 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