Nondecreasing analytic radius for the KdV equation with a weakly damping. (February 2022)

• Record Type: Journal Article
• Authors: Wang, Ming
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: 35Q55 -- 35A20; KdV equation -- Analytic radius -- Damped effect; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112653
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the long time behavior of the analytic radius for the solution of the KdV equation with an analytic initial data on the real line. The best result in the references shows that the analytic radius has a polynomial decay lower bound, which means the analytic radius may shrink to zero as time goes to infinity. In this note we prove that, for the KdV equation with some damping, the analytic radius has a fixed positive lower bound uniformly for all time.