On Gevrey regularity of solutions for inhomogeneous nonlinear moment partial differential equations

TL;DR

This paper studies the Gevrey regularity of formal solutions to a class of nonlinear moment partial differential equations with inhomogeneity, extending previous results for linear and standard nonlinear PDEs by analyzing the Newton polygon structure.

Contribution

It generalizes existing regularity results to nonlinear moment PDEs with inhomogeneity, using geometric analysis of the Newton polygon.

Findings

Gevrey regularity depends on the Newton polygon structure.

Results extend known regularity for linear and standard nonlinear PDEs.

Provides a framework for analyzing nonlinear moment PDEs.

Abstract

In this article we investigate Gevrey regularity of formal power series solutions for a certain class of nonlinear moment partial differential equations, the inhomogeneity of which is $\sigma$-Gevrey with respect to the time variable $t$ for a fixed $\sigma\ge 0$. The results are achieved by analyzing the geometric structure of the Newton polygon associated with the equation and are a generalization of similar results obtained for standard nonlinear partial differential equations as well as linear moment differential equations.