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On the Parametric Stokes Phenomenon for Solutions of Singularly Perturbed Linear Partial Differential Equations
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-86, 86 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-31
Country of Publication
Egypt
No. of Pages
86
Main Subjects
Abstract EN
We study a family of singularly perturbed linear partial differential equations with irregular type ϵt2∂t∂zSXi(t,z,ϵ)+(ϵt+1)∂zSXi(t,z,ϵ)=∑(s,k0,k1)∈?bs,k0,k1(z,ϵ)ts∂tk0∂zk1Xi(t,z,ϵ) in the complex domain.
In a previous work, Malek (2012), we have given sufficient conditions under which the Borel transform of a formal solution to the above mentioned equation with respect to the perturbation parameter ϵ converges near the origin in ℂ and can be extended on a finite number of unbounded sectors with small opening and bisecting directions, say κi∈[0,2π), 0≤i≤ν−1 for some integer ν≥2.
The proof rests on the construction of neighboring sectorial holomorphic solutions to the first mentioned equation whose differences have exponentially small bounds in the perturbation parameter (Stokes phenomenon) for which the classical Ramis-Sibuya theorem can be applied.
In this paper, we introduce new conditions for the Borel transform to be analytically continued in the larger sectors {ϵ∈ℂ∗/arg(ϵ)∈(κi,κi+1)}, where it develops isolated singularities of logarithmic type lying on some half lattice.
In the proof, we use a criterion of analytic continuation of the Borel transform described by Fruchard and Schäfke (2011) and is based on a more accurate description of the Stokes phenomenon for the sectorial solutions mentioned above.
American Psychological Association (APA)
Malek, Stéphane. 2012. On the Parametric Stokes Phenomenon for Solutions of Singularly Perturbed Linear Partial Differential Equations. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-86.
https://search.emarefa.net/detail/BIM-509062
Modern Language Association (MLA)
Malek, Stéphane. On the Parametric Stokes Phenomenon for Solutions of Singularly Perturbed Linear Partial Differential Equations. Abstract and Applied Analysis No. 2012 (2012), pp.1-86.
https://search.emarefa.net/detail/BIM-509062
American Medical Association (AMA)
Malek, Stéphane. On the Parametric Stokes Phenomenon for Solutions of Singularly Perturbed Linear Partial Differential Equations. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-86.
https://search.emarefa.net/detail/BIM-509062
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509062