Boundary layer expansions for initial value problems with two complex time variables
Abstract We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequa...
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| Format: | Article |
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SpringerOpen
2020-01-01
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| Series: | Advances in Difference Equations |
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| Online Access: | https://doi.org/10.1186/s13662-020-2496-3 |
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doaj-ae9503d5e7b042f68f0b4677aa7f06b02021-01-10T12:52:19ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020112410.1186/s13662-020-2496-3Boundary layer expansions for initial value problems with two complex time variablesA. Lastra0S. Malek1Departamento de Física y Matemáticas, University of AlcaláLaboratoire Paul Painlevé, University of Lille 1Abstract We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequate domains. The asymptotic representation leans on the cohomological approach determined by the Ramis–Sibuya theorem.https://doi.org/10.1186/s13662-020-2496-3Asymptotic expansionBorel–Laplace transformFourier transformInitial value problemFormal power seriesBoundary layer |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. Lastra S. Malek |
| spellingShingle |
A. Lastra S. Malek Boundary layer expansions for initial value problems with two complex time variables Advances in Difference Equations Asymptotic expansion Borel–Laplace transform Fourier transform Initial value problem Formal power series Boundary layer |
| author_facet |
A. Lastra S. Malek |
| author_sort |
A. Lastra |
| title |
Boundary layer expansions for initial value problems with two complex time variables |
| title_short |
Boundary layer expansions for initial value problems with two complex time variables |
| title_full |
Boundary layer expansions for initial value problems with two complex time variables |
| title_fullStr |
Boundary layer expansions for initial value problems with two complex time variables |
| title_full_unstemmed |
Boundary layer expansions for initial value problems with two complex time variables |
| title_sort |
boundary layer expansions for initial value problems with two complex time variables |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2020-01-01 |
| description |
Abstract We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequate domains. The asymptotic representation leans on the cohomological approach determined by the Ramis–Sibuya theorem. |
| topic |
Asymptotic expansion Borel–Laplace transform Fourier transform Initial value problem Formal power series Boundary layer |
| url |
https://doi.org/10.1186/s13662-020-2496-3 |
| work_keys_str_mv |
AT alastra boundarylayerexpansionsforinitialvalueproblemswithtwocomplextimevariables AT smalek boundarylayerexpansionsforinitialvalueproblemswithtwocomplextimevariables |
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1724342246970490880 |