Gevrey regularity of the solutions of inhomogeneous nonlinear partial differential equations

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations Pub Date : 2023-01-19 DOI:10.58997/ejde.2023.06

Pascal Remy

引用次数: 1

Abstract

In this article, we are interested in the Gevrey properties of the formal power series solutions in time of some inhomogeneous nonlinear partial differential equations with analytic coefficients at the origin of Cn+1. We systematically examine the cases where the inhomogeneity is s-Gevrey for any s≥0, in order to carefully distinguish the influence of the data (and their degree of regularity) from that of the equation (and its structure). We thus prove that we have a noteworthy dichotomy with respect to a nonnegative rational number sc fully determined by the Newton polygon of a convenient associated linear partial differential equation: for any s≥sc, the formal solutions and the inhomogeneity are simultaneously s-Gevrey; for any s

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非齐次非线性偏微分方程解的Gevrey正则性

在本文中，我们对Cn+1原点处具有解析系数的非齐次非线性偏微分方程的形式幂级数解在时间上的Gevrey性质感兴趣。对于任意s≥0，我们系统地检查了不均匀性为s- gevrey的情况，以便仔细区分数据(及其规律性程度)与方程(及其结构)的影响。由此证明了一个非负有序数sc完全由一个方便关联线性偏微分方程的牛顿多边形决定的一个值得注意的二分性:对于任意s≥sc，其形式解和非齐次性同时为s- gevrey;对于任意s

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.

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