ArticleOriginal scientific text
Title
Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
Authors 1, 2
Affiliations
- Institute of Mathematics, Kraków Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Abstract
We consider a nonlinear Laplace equation Δu = f(x,u) in two variables. Following the methods of B. Braaksma [Br] and J. Ecalle used for some nonlinear ordinary differential equations we construct first a formal power series solution and then we prove the convergence of the series in the same class as the function f in x.
Keywords
Borel resummation, formal solutions, Laplace equation
Bibliography
- [Br] B. Braaksma, Multisummability of formal power series solutions of nonlinear meromorphic differential equations, Ann. Inst. Fourier (Grenoble) 42 (1992), 517-541.
- [Sz-Zie] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type PDEs, Kluwer, 1992.
- [Zie1] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).
- [Zie2] B. Ziemian, Leray residue formula and asymptotics of solutions to constant coefficient PDEs, Topol. Methods Nonlinear Anal. 3 (1994), 257-293.
Pages:
31-41
Main language of publication
English
Received
1995-10-02
Accepted
1996-10-10
Published
1997
Exact and natural sciences