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.
- Formal solution
- Linear partial differential equation
- Non-Kowalevskian equation
ASJC Scopus subject areas
- Applied Mathematics