Browsing by Subject "convolution equations"
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Item type:Article, Access status: Open Access , Analytic continuation of solutions of some nonlinear convolution partial differential equations(2015) Tahara, HidetoshiThe 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.