Gevrey Estimates of Formal Solutions for Certain Moment Partial Differential Equations with Variable Coefficients-Reference-Cited by-同舟云学术

Gevrey Estimates of Formal Solutions for Certain Moment Partial Differential Equations with Variable Coefficients

Published:2020-07-21 Issue:2 Volume:27 Page:355-370
ISSN:1079-2724
Container-title:Journal of Dynamical and Control Systems
language:en
Short-container-title:J Dyn Control Syst

Author:

Suwińska Maria^ORCID

Abstract

AbstractThe goal of this paper is to investigate Gevrey properties of formal solutions of certain generalized linear partial differential equations with variable coefficients. In particular, we extend the notion of moment partial differential equations to include differential operators that are not connected with kernel functions. Using the modified version of Nagumo norms and the properties of the Newton polygon we compute the Gevrey estimate for formal solutions of such generalized partial differential equations.

Publisher

Springer Science and Business Media LLC

Subject

Control and Optimization,Numerical Analysis,Algebra and Number Theory,Control and Systems Engineering

Link

https://link.springer.com/content/pdf/10.1007/s10883-020-09504-3.pdf

Reference11 articles.

1. Balser W. Formal power series and linear systems of meromorphic ordinary differential equations. New York: Springer; 2000.

2. Balser W, Loday-Richaud M. Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables. Advances in Dynamical Systems and Applications 2009;4(2):159–177.

3. Balser W, Yoshino M. Gevrey order of formal power series solutions of inhomogeneous partial differential equations with constant coefficients. Funkcial Ekvac 2010;53:411–434.

4. Lastra M, Michalik S, Suwińska M. 2020. Estimates of formal solutions for some generalized moment partial differential equations. arXiv:https://arxiv.org/abs/1911.11998.

5. Michalik S. Analytic solutions of moment partial differential equations with constant coefficients. Funkcial Ekvac 2013;56:19–50.

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Linear Moment Partial Differential Equations;Lecture Notes in Mathematics;2024

2. Solutions of linear systems of moment differential equations via generalized matrix exponentials;Journal of Differential Equations;2023-11

3. Some notes on moment partial differential equations. Application to fractional functional equations;Recent Trends in Formal and Analytic Solutions of Diff. Equations;2023

4. Summability of formal solutions for a family of linear moment integro-differential equations;Recent Trends in Formal and Analytic Solutions of Diff. Equations;2023

5. Multisummability of Formal Solutions for a Family of Generalized Singularly Perturbed Moment Differential Equations;Results in Mathematics;2022-12-30