Parametric Borel summability for some semilinear system of partial differential equations

• Autorzy: Yamazawa H. , Yoshino M.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.5.825

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Borel summability; singular perturbation; Euler type operator

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 5
• Strony: 825--845
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Yamazawa H.

• Shibaura Institute of Technology College of Engineer and Design Minuma-ku, Saitama-shi, Saitama 337-8570, Japan

autor

Yoshino M.

• Department of Mathematics Graduate School of Science Hiroshima University 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan

Bibliografia

• [1] W. Balser, Formal power series and linear systems of meromorphic ordinary differential equations, Universitext, Springer-Verlag, New York (2000).
• [2] W. Balser, V. Kostov, Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002) 3, 313-322.
• [3] W. Balser, M. Loday-Richaud, Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables, Adv. Dynam. Syst. Appl. 4 (2009), 159-177.
• [4] W. Balser, J. Mozo-Fernandez, Multisummability of formal solutions of singular pertur­bation problems, J. Differential Equations 183 (2002), 526-545.
• [5] K. Ichinobe, Integral representation for Borel sum of divergent solution to a certain non-Kowalevski type equation, Publ. Res. Inst. Math. Sci. 39 (2003), 657-693.
• [6] Z. Luo, H. Chen, C. Zhang, Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations, Ann. Inst. Fourier 62 (2012) 2, 571-618.
• [7] A. Lastra, S. Malek, J. Sanz, On Gevrey solutions of threefold singular nonlinear partial differential equations, J. Differential Equations 255 (2013) 10, to appear.
• [8] D.A. Lutz, M. Miyake, R. Schafke, On the Borel summability of divergent solutions of the heat equation, Nagoya Math. J. 154 (1999), 1-29.
• [9] S. Malek, On the summability of formal solutions for doubly singular nonlinear partial differential equations, J. Dynam. Control. Syst. 18 (2012), 45-82.
• [10] S. Michalik, Summability of formal solutions to the n-dimensional inhomogeneous heat equation, J. Math. Anal. Appl. 347 (2008), 323-332.
• [11] S. Ouchi, Multisummability of formal power series solutions of nonlinear partial differ­ential equations in complex domains, Asympt. Anal. 47 (2006) 3-4, 187-225.