Abstract
The paper considers the Cauchy problem for linear partial differential equations of non-Kowalevskian type in the complex domain. It is shown that if the Cauchy data are entire functions of a suitable order, the problem has a formal solution which is multisummable. The precise bound of the admissible order of entire functions is described in terms of the Newton polygon of the equation.
| Original language | English |
|---|---|
| Pages (from-to) | 3592-3637 |
| Number of pages | 46 |
| Journal | Journal of Differential Equations |
| Volume | 255 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2013 Nov 15 |
Keywords
- Formal solution
- Linear partial differential equation
- Multisummability
- Non-Kowalevskian equation
- Primary
- Secondary
ASJC Scopus subject areas
- Analysis
- Applied Mathematics