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On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays

Author

Listed:
  • Alberto Lastra
  • Stéphane Malek

Abstract

We study a family of singularly perturbed -difference-differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter . Moreover, we achieve the existence of a common formal power series in which represents each actual solution and establish -Gevrey estimates involved in this representation. The proof of the main result rests on a new version of the so-called Malgrange-Sibuya theorem regarding -Gevrey asymptotics. A particular Dirichlet like series is studied on the way.

Suggested Citation

  • Alberto Lastra & Stéphane Malek, 2013. "On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-18, November.
    • Handle: RePEc:hin:jnlaaa:723040
    DOI: 10.1155/2013/723040
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    Cited by:

    1. David W. Pravica & Njinasoa Randriampiry & Michael J. Spurr, 2014. "Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. David W. Pravica & Njinasoa Randriampiry & Michael J. Spurr, 2022. "Solutions of a Class of Multiplicatively Advanced Differential Equations II: Fourier Transforms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
    3. David W. Pravica & Njinasoa Randriampiry & Michael J. Spurr, 2024. "Solutions of Inhomogeneous Multiplicatively Advanced ODEs and PDEs with a q‐Fredholm Theory and Applications to a q‐Advanced Schrödinger Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).

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