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

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Lastra A., Malek S., Sanz J.

Banach Center Publications

2012

tom 97

nr 1

73-90

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.

Ograniczanie wyników

1 Banach Center Publications

1 Lastra A.

1 Malek S.

1 Sanz J.

1 2012

Wyniki wyszukiwania

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