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On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference differential initial value Cauchy problems (1607.01986v1)
Published 7 Jul 2016 in math.AP and math.CV
Abstract: We study the asymptotic behavior of the solutions related to a singularly perturbed q-difference-differential problem in the complex domain. The analytic solution can be splitted according to the nature of the equation and its geometry so that both, Gevrey and q-Gevrey asymptotic phenomena are observed and can be distinguished, relating the analytic and the formal solution. The proof leans on a two level novel version of Ramis-Sibuya theorem under Gevrey and q-Gevrey orders.