Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms

Abstract

Abstract This work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows one to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work (Lastra and Malek in Adv. Differ. Equ. 2020:20, 2020) by the last two authors. The result leans on the application of a fixed point argument and the classical Ramis–Sibuya theorem.

Keywords

• Asymptotic expansion
• Borel–Laplace transform
• Fourier transform
• Initial value problem
• Formal power series
• Nonlinear partial differential equation