Opuscula Math. 35, no. 5 (2015), 739-773
http://dx.doi.org/10.7494/OpMath.2015.35.5.739

Opuscula Mathematica

# Analytic continuation of solutions of some nonlinear convolution partial differential equations

Hidetoshi Tahara

Abstract. 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.

Keywords: convolution equations, partial differential equations, analytic continuation, summability, sector.

Mathematics Subject Classification: 45K05, 45G10, 35A20.

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• Hidetoshi Tahara
• Sophia University, Department of Information and Communication Sciences, Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan
• Communicated by P.A. Cojuhari.
• Revised: 2014-12-12.
• Accepted: 2015-01-23.
• Published online: 2015-04-27.