RT info:eu-repo/semantics/article
T1 On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
A1 Lastra Sedano, Alberto
A1 Sanz, Javier
A1 Malek, Stephane
K1 q-Difference-differential equations
K1 q-Laplace transform
K1 Formal power series solutions
K1 q-Gevrey asymptotic expansions
K1 Small divisors
K1 Fuchsian and irregular singularities
K1 Matemáticas
K1 Mathematics
AB We consider a Cauchy problem for some family of linear q-difference-differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables X (t, z) for given formal power series initial conditions. Under suitable conditions and by the application of certain q-Borel and Laplace transforms (introduced by J.-P. Ramis and C. Zhang), we are able to deal with the small divisors phenomenon caused by the Fuchsian singularity, and to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion in t, uniformly for z in the compact sets of , is X (t, z) . The small divisorsʼ effect is an increase in the order of q-exponential growth and the appearance of a power of the factorial in the corresponding q-Gevrey bounds in the asymptotics.
PB Elsevier
SN 0022-0396
YR 2012
FD 2012-05-15
LK http://hdl.handle.net/10017/41470
UL http://hdl.handle.net/10017/41470
LA eng
DS MINDS@UW
RD 19-abr-2024