Boundary layer expansions for initial value problems with two complex time variables

Abstract

Abstract We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter ϵ. We construct inner and outer solutions of the problem and relate them to asymptotic representations via Gevrey asymptotic expansions with respect to ϵ in adequate domains. The asymptotic representation leans on the cohomological approach determined by the Ramis–Sibuya theorem.

Keywords

• Asymptotic expansion
• Borel–Laplace transform
• Fourier transform
• Initial value problem
• Formal power series
• Boundary layer