On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities

Alberto Lastra, Stéphane Malek, and Javier Sanz. "On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities." Banach Center Publications 97.1 (2012): 73-90. <http://eudml.org/doc/282341>.

@article{AlbertoLastra2012,
abstract = {This work is devoted to the study of a Cauchy problem for a certain family of q-difference-differential equations having Fuchsian and irregular singularities. For given formal initial conditions, we first prove the existence of a unique formal power series X̂(t,z) solving the problem. Under appropriate conditions, q-Borel and q-Laplace techniques (firstly developed by J.-P. Ramis and C. Zhang) help us in order to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion in t, uniformly for z in the compact sets of ℂ, is X̂(t,z). The small divisors phenomenon owing to the Fuchsian singularity causes an increase in the order of q-exponential growth and the appearance of a subexponential Gevrey growth in the asymptotics.},
author = {Alberto Lastra, Stéphane Malek, Javier Sanz},
journal = {Banach Center Publications},
keywords = {q-difference-differential equations; q-Laplace transform; formal power series solutions; q-Gevrey asymptotic expansions; small divisors; Fuchsian singularities; irregular singularities},
language = {eng},
number = {1},
pages = {73-90},
title = {On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities},
url = {http://eudml.org/doc/282341},
volume = {97},
year = {2012},
}

TY - JOUR
AU - Alberto Lastra
AU - Stéphane Malek
AU - Javier Sanz
TI - On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities
JO - Banach Center Publications
PY - 2012
VL - 97
IS - 1
SP - 73
EP - 90
AB - This work is devoted to the study of a Cauchy problem for a certain family of q-difference-differential equations having Fuchsian and irregular singularities. For given formal initial conditions, we first prove the existence of a unique formal power series X̂(t,z) solving the problem. Under appropriate conditions, q-Borel and q-Laplace techniques (firstly developed by J.-P. Ramis and C. Zhang) help us in order to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion in t, uniformly for z in the compact sets of ℂ, is X̂(t,z). The small divisors phenomenon owing to the Fuchsian singularity causes an increase in the order of q-exponential growth and the appearance of a subexponential Gevrey growth in the asymptotics.
LA - eng
KW - q-difference-differential equations; q-Laplace transform; formal power series solutions; q-Gevrey asymptotic expansions; small divisors; Fuchsian singularities; irregular singularities
UR - http://eudml.org/doc/282341
ER -