Analytic continuation of solutions of some nonlinear convolution partial differential equations

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