On the Existence and Uniqueness of the Formal Solution to a Singular Partial Differential Equation
- https://doi.org/10.2991/icmmita-16.2016.241How to use a DOI?
- Formal Power Series Solution; Gevrey Order in a Monomial; Asymptotic Expansion in a Monomial
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).
- © 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 -