Opuscula Math. 35, no. 5 (2015), 825-845
http://dx.doi.org/10.7494/OpMath.2015.35.5.825
Opuscula Mathematica
Parametric Borel summability for some semilinear system of partial differential equations
Hiroshi Yamazawa
Masafumi Yoshino
Abstract. In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \(n\) independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.
Keywords: Borel summability, singular perturbation, Euler type operator.
Mathematics Subject Classification: 35C10, 45E10, 35Q15.
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- Hiroshi Yamazawa
- Shibaura Institute of Technology, College of Engineer and Design, Minuma-ku, Saitama-shi, Saitama 337-8570, Japan
- Masafumi Yoshino
- Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8526, Japan
- Communicated by Theodore A. Burton.
- Received: 2013-11-26.
- Revised: 2015-03-19.
- Accepted: 2015-03-20.
- Published online: 2015-04-27.
