Open AccessAnalytic continuation of solutions of some nonlinear convolution partial differential equations
Author(s) -
Hidetoshi Tahara
Publication year - 2015
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2015.35.5.739
Subject(s) - mathematics , holomorphic function , analytic continuation , nonlinear system , extension (predicate logic) , convolution (computer science) , mathematical analysis , continuation , infinity , partial differential equation , first order partial differential equation , physics , quantum mechanics , machine learning , computer science , artificial neural network , programming language
The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector