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On Parametric Gevrey Asymptotics for Some Initial Value Problems in Two Asymmetric Complex Time Variables

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Abstract

We study a family of nonlinear initial value problem for partial differential equations in the complex domain under the action of two asymmetric time variables. Different Gevrey bounds and multisummability results are obtained depending on each element of the family, providing a more complete picture on the asymptotic behavior of the solutions of PDEs in the complex domain in several complex variables. The main results lean on a fixed point argument in certain Banach space in the Borel plane, together with a Borel summability procedure and the action of different Ramis–Sibuya type theorems.

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Author information

Correspondence to A. Lastra.

Additional information

A. Lastra and S. Malek are partially supported by the project MTM2016-77642-C2-1-P of Ministerio de Economía y Competitividad, Spain.

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Lastra, A., Malek, S. On Parametric Gevrey Asymptotics for Some Initial Value Problems in Two Asymmetric Complex Time Variables. Results Math 73, 155 (2018). https://doi.org/10.1007/s00025-018-0914-6

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Keywords

  • Asymptotic expansion
  • Borel–Laplace transform
  • Fourier transform
  • initial value problem
  • formal power series
  • nonlinear integro-differential equation
  • nonlinear partial differential equation
  • singular perturbation

Mathematics Subject Classification

  • 35C10
  • 35C20