Estimates of formal solutions for some generalized moment partial differential equations

TL;DR

This paper develops generalized methods for estimating formal solutions of certain moment partial differential equations using advanced tools like Newton polygons and divergent norms, broadening the scope of previous approaches.

Contribution

It introduces a generalized framework for formal moment differentiation that includes a wider class of operators by relaxing Gevrey sequence constraints.

Findings

Derived estimates for formal solutions of generalized PDEs.

Extended the class of operators applicable in moment PDE analysis.

Utilized Newton polygon and divergent norms for solution estimation.

Abstract

Using increasing sequences of real numbers, we generalize the idea of formal moment differentiation first introduced by W. Balser and M. Yoshino. Slight departure from the concept of Gevrey sequences enables us to include a wide variety of operators in our study. Basing our approach on tools such as the Newton polygon and divergent formal norms, we obtain estimates for formal solutions of certain families of generalized linear moment partial differential equations with constant and time variable coefficients.