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

• Autorzy: Alberto Lastra , Stéphane Malek , Javier Sanz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 34M25: Formal solutions, transform techniques
• 34K25: Asymptotic theory
• 34M30: Asymptotics, summation methods
• 33E30: Other functions coming from differential, difference and integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2012
• Tom: 97
• Numer: 1
• Strony: 73-90

Daty

wydano

2012

Twórcy

autor

Alberto Lastra

• Facultad de Ciencias, Universidad de Valladolid, Calle del Doctor Mergelina s/n, 47011 Valladolid, Spain

autor

Stéphane Malek

• UFR de Mathématiques, Université Lille 1, Cité Scientifique M2, 59655 Villeneuve d'Ascq Cedex, France

autor

Javier Sanz

• Facultad de Ciencias, Universidad de Valladolid, Calle del Doctor Mergelina s/n, 47011 Valladolid, Spain

Identyfikatory

DOI

10.4064/bc97-0-5