On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities
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 appl...
| Authors: | ; ; |
|---|---|
| Format: | Article |
| Publication date: | 2012 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/41470 |
| Online Access: | http://hdl.handle.net/10017/41470 https://dx.doi.org/10.1016/j.jde.2012.01.038 |
| Access Level: | Open access |
| Keyword: | q-Difference-differential equations q-Laplace transform Formal power series solutions q-Gevrey asymptotic expansions Small divisors Fuchsian and irregular singularities Matemáticas Mathematics |
| _version_ | 1878733409989165056 |
|---|---|
| author | Lastra Sedano, Alberto|||0000-0002-4012-6471 |
| author2 | Sanz, Javier Malek, Stephane |
| author2_role | author author |
| author_browse | Lastra Sedano, Alberto|||0000-0002-4012-6471 Malek, Stephane Sanz, Javier |
| author_facet | Lastra Sedano, Alberto|||0000-0002-4012-6471 Sanz, Javier Malek, Stephane |
| author_role | author |
| collection | e_Buah Biblioteca Digital Universidad de Alcalá |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_559665cb4a80ae953573e54ffc00a3c5 |
| institution | Universidad de Alcalá (UAH) |
| instname_str | Universidad de Alcalá (UAH) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ebuah.uah.es:10017/41470 |
| publishDate | 2012 |
| publishDateSort | 2012 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | e_Buah Biblioteca Digital Universidad de Alcalá |
| spelling | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities Lastra Sedano, Alberto|||0000-0002-4012-6471 Sanz, Javier Malek, Stephane q-Difference-differential equations q-Laplace transform Formal power series solutions q-Gevrey asymptotic expansions Small divisors Fuchsian and irregular singularities Matemáticas Mathematics 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. Elsevier http://hdl.handle.net/10017/41470 https://dx.doi.org/10.1016/j.jde.2012.01.038 |
| spellingShingle | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities Lastra Sedano, Alberto|||0000-0002-4012-6471 q-Difference-differential equations q-Laplace transform Formal power series solutions q-Gevrey asymptotic expansions Small divisors Fuchsian and irregular singularities Matemáticas Mathematics |
| title | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities |
| title_full | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities |
| title_fullStr | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities |
| title_full_unstemmed | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities |
| title_short | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities |
| title_sort | On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities |
| topic | q-Difference-differential equations q-Laplace transform Formal power series solutions q-Gevrey asymptotic expansions Small divisors Fuchsian and irregular singularities Matemáticas Mathematics |
| topic_facet | q-Difference-differential equations q-Laplace transform Formal power series solutions q-Gevrey asymptotic expansions Small divisors Fuchsian and irregular singularities Matemáticas Mathematics |
| url | http://hdl.handle.net/10017/41470 https://dx.doi.org/10.1016/j.jde.2012.01.038 |