On complex singularity analysis for some linear partial differential equations in C3
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/41436DOI: 10.1155/2013/394564
ISSN: 1085-3375
Publisher
Hindawi
Date
2013-11-07Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Lastra, A., Malek, S. & Stenger, C. 2013, “On complex singularity analysis for some linear partial differential equations in C3”, Abstract and Applied Analysis, vol. 2013, art. no. 394564.
Project
info:eu-repo/grantAgreement/MINECO//MTM2012-31439/ES/ANALISIS DE PERTURBACIONES SINGULARES: ESTUDIO ASINTOTICO, CAPAS LIMITE Y FENOMENOS MULTIESCALA/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1155/2013/394564Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
We investigate the existence of local holomorphic solutions Y of linear partial differential equations in three complex variableswhose coefficients are holomorphic on some polydisc in C2 outside some singular set Theta. The coefficients are written as linearcombinations of powers of a solution X of some first-order nonlinear partial differential equation following an idea, we haveinitiated in a previous work (Malek and Stenger 2011). The solutions Y are shown to develop singularities along Theta with estimatesof exponential type depending on the growth's rate of X near the singular set.We construct these solutions with the help of seriesof functions with infinitely many variables which involve derivatives of all orders of X in one variable. Convergence and boundsestimates of these series are studied using a majorant series method which leads to an auxiliary functional equation that containsdifferential operators in infinitely many variables. Using a fixed point argument, we show that these functional equations actuallyhave solutions in some Banach spaces of formal power series.
Files in this item
Files | Size | Format |
|
---|---|---|---|
On_complex_Lastra_AAA_2013.pdf | 2.132Mb |
|
Files | Size | Format |
|
---|---|---|---|
On_complex_Lastra_AAA_2013.pdf | 2.132Mb |
|
Collections
- MATEMATIC - Artículos [172]