Analytic continuation of solutions of some nonlinear convolution partial differential equations
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 h...
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AGH Univeristy of Science and Technology Press
2015-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol35/5/art/opuscula_math_3539.pdf |
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doaj-4821b1480fec4f489090023c8cd0c9932020-11-24T22:45:23ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742015-01-01355739773http://dx.doi.org/10.7494/OpMath.2015.35.5.7393539Analytic continuation of solutions of some nonlinear convolution partial differential equationsHidetoshi Tahara0Sophia University, Department of Information and Communication Sciences, Kioicho, Chiyoda-ku, Tokyo 102-8554, JapanThe 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.http://www.opuscula.agh.edu.pl/vol35/5/art/opuscula_math_3539.pdfconvolution equationspartial differential equationsanalytic continuationsummabilitysector |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hidetoshi Tahara |
| spellingShingle |
Hidetoshi Tahara Analytic continuation of solutions of some nonlinear convolution partial differential equations Opuscula Mathematica convolution equations partial differential equations analytic continuation summability sector |
| author_facet |
Hidetoshi Tahara |
| author_sort |
Hidetoshi Tahara |
| title |
Analytic continuation of solutions of some nonlinear convolution partial differential equations |
| title_short |
Analytic continuation of solutions of some nonlinear convolution partial differential equations |
| title_full |
Analytic continuation of solutions of some nonlinear convolution partial differential equations |
| title_fullStr |
Analytic continuation of solutions of some nonlinear convolution partial differential equations |
| title_full_unstemmed |
Analytic continuation of solutions of some nonlinear convolution partial differential equations |
| title_sort |
analytic continuation of solutions of some nonlinear convolution partial differential equations |
| publisher |
AGH Univeristy of Science and Technology Press |
| series |
Opuscula Mathematica |
| issn |
1232-9274 |
| publishDate |
2015-01-01 |
| description |
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. |
| topic |
convolution equations partial differential equations analytic continuation summability sector |
| url |
http://www.opuscula.agh.edu.pl/vol35/5/art/opuscula_math_3539.pdf |
| work_keys_str_mv |
AT hidetoshitahara analyticcontinuationofsolutionsofsomenonlinearconvolutionpartialdifferentialequations |
| _version_ |
1725688819187974144 |