On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables

TL;DR

This paper investigates the asymptotic behavior of solutions to nonlinear PDEs with two asymmetric complex time variables, establishing Gevrey bounds and multisummability results using fixed point and Borel summability methods.

Contribution

It introduces new Gevrey bounds and multisummability results for a family of nonlinear PDEs in complex variables, enhancing understanding of their asymptotic solutions.

Findings

Different Gevrey bounds depending on family elements

Multisummability results for solutions in complex domain

Application of Ramis-Sibuya theorems in analysis

Abstract

We study a family of nonlinear initial value partial differential equations in the complex domain under the action of two asymmetric time variables. Different Gevrey bounds and multisummability results are obtain 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.