Strongly Regular Multi-level Solutions of Singularly Perturbed Linear Partial Differential Equations

@article{Lastra2015StronglyRM,
  title={Strongly Regular Multi-level Solutions of Singularly Perturbed Linear Partial Differential Equations},
  author={Alberto Lastra and Stephane Malek and Javier Sanz},
  journal={Results in Mathematics},
  year={2015},
  volume={70},
  pages={581-614}
}
We study the asymptotic behavior of the solutions related to a family of singularly perturbed partial differential equations in the complex domain. The analytic solutions are asymptotically represented by a formal power series in the perturbation parameter. The geometry of the problem and the nature of the elements involved in it give rise to different asymptotic levels related to the so-called strongly regular sequences. The result leans on a novel version of a multi-level Ramis–Sibuya theorem… 
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Background Citations
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Methods Citations
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9 Citations

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Citation Type

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References

SHOWING 1-10 OF 33 REFERENCES
Multi-level Gevrey solutions of singularly perturbed linear partial differential equations
We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions obtained by means of…
On the summability of formal solutions for doubly singular nonlinear partial differential equations
We study Gevrey asymptotic properties of solutions of singularly perturbed singular nonlinear partial differential equations of irregular type in the complex domain. We construct actual holomorphic…
Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations
Summability of formal solutions of linear partial differential equations with divergent initial data
On Gevrey solutions of threefold singular nonlinear partial differential equations
On the exact WKB analysis of singularly perturbed ordinary differential equations at an irregular singular point (Recent development of microlocal analysis and asymptotic analysis)
We announce the results of [K]. We present decomposition of WKB solutions to monomially summable series at an irregular singular point of singularly perturbed ordinary differential equations when the…
Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations
Basic Properties of Solutions.- Singularities of First Kind.- Highest-Level Formal Solutions.- Asymptotic Power Series.- Integral Operators.- Summable Power Series.- Cauchy-Heine Transform.-…
Some Notes on the Multi-Level Gevrey Solutions of Singularly Perturbed Linear Partial Differential Equations
This paper is a slightly modified, abridged version of the work (Lastra and Malek, Adv Differ Equ 21:767–800, 2016). It deals with some questions made to the authors during the conference Analytic,…
Analytic Solutions of Moment Partial Differential Equations with Constant Coefficients
We consider the Cauchy problem for linear moment partial differential equations with constant coefficients in two complex variables. We construct an integral representation of the solution of this…
On Gevrey functional solutions of partial differential equations with Fuchsian and irregular singularities
We construct formal power series solutions of nonlinear partial integro-differential equations with Fuchsian and irregular singularities at the origin of $$ \mathbb{C}^2 $$ for given initial…
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