Affiliation:
1. Laboratoire Paul Painlevé , University of Lille , 59655 Villeneuve d’Ascq cedex , France
Abstract
Abstract
We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane with respect to time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.
Subject
Applied Mathematics,Numerical Analysis,Analysis
Reference15 articles.
1. W. Balser,
Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations,
Universitext,
Springer, New York, 2000.
2. B. Braaksma and L. Stolovitch,
Small divisors and large multipliers,
Ann. Inst. Fourier (Grenoble) 57 (2007), no. 2, 603–628.
3. O. Costin and S. Tanveer,
Short time existence and Borel summability in the Navier–Stokes equation in
ℝ
3
\mathbb{R}^{3}
,
Comm. Partial Differential Equations 34 (2009), no. 7–9, 785–817.
4. P.-F. Hsieh and Y. Sibuya,
Basic Theory of Ordinary Differential Equations,
Universitext,
Springer, New York, 1999.
5. A. Lastra and S. Malek,
On parametric Gevrey asymptotics for singularly perturbed partial differential equations with delays,
Abstr. Appl. Anal. 2013 (2013), Article ID 723040.