Proceedings of the 2016 4th International Conference on Machinery, Materials and Information Technology Applications

On the Existence and Uniqueness of the Formal Solution to a Singular Partial Differential Equation

Authors
Pingli Li, Sihui Li
Corresponding Author
Pingli Li
Available Online January 2017.
DOI
https://doi.org/10.2991/icmmita-16.2016.241How to use a DOI?
Keywords
Formal Power Series Solution; Gevrey Order in a Monomial; Asymptotic Expansion in a Monomial
Abstract

According to the theory used in researching certain type of doubly singular differential equations, by computing directly, we find out that a singular partial differential equation in two complex variables has a unique formal power series solution which is in a special form and whose coefficients can be worked out explicitly. By estimating coefficients of the solution, we prove this formal solution is 1-Gevrey in a monomial. This gives a way to study Gevrey order in a monomial for formal solutions to certain classes of differential equations (or systems).

Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2016 4th International Conference on Machinery, Materials and Information Technology Applications
Series
Advances in Computer Science Research
Publication Date
January 2017
ISBN
978-94-6252-285-5
ISSN
2352-538X
DOI
https://doi.org/10.2991/icmmita-16.2016.241How to use a DOI?
Copyright
© 2017, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Pingli Li
AU  - Sihui Li
PY  - 2017/01
DA  - 2017/01
TI  - On the Existence and Uniqueness of the Formal Solution to a Singular Partial Differential Equation
BT  - Proceedings of the 2016 4th International Conference on Machinery, Materials and Information Technology Applications
PB  - Atlantis Press
SN  - 2352-538X
UR  - https://doi.org/10.2991/icmmita-16.2016.241
DO  - https://doi.org/10.2991/icmmita-16.2016.241
ID  - Li2017/01
ER  -