RT info:eu-repo/semantics/article T1 On multiscale Gevrey and q-Gevrey asymptotics for some linear q-difference-differential initial value Cauchy problems A1 Lastra Sedano, Alberto A1 Malek, Stephane K1 Asymptotic expansion K1 Borel-Laplace transform K1 Fourier transform K1 Cauchy problem K1 Formal power series K1 Nonlinear integro-differential equation K1 Nonlinear partial differential equation K1 Singular perturbation K1 Matemáticas K1 Mathematics AB 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. PB Taylor & Francis SN 1023-6198 YR 2017 FD 2017-06-12 LK http://hdl.handle.net/10017/41440 UL http://hdl.handle.net/10017/41440 LA eng DS MINDS@UW RD 29-mar-2024