Opuscula Mathematica
Opuscula Math. 35, no. 5 (), 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


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.
Cite this article as:
Hidetoshi Tahara, Analytic continuation of solutions of some nonlinear convolution partial differential equations, Opuscula Math. 35, no. 5 (2015), 739-773, http://dx.doi.org/10.7494/OpMath.2015.35.5.739
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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