Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation

被引：3

作者：

Chu, Jixun ^{[1
]}

Coron, Jean-Michel ^{[2
,3
]}

Shang, Peipei ^{[2
,4
,5
]}

Tang, Shu-Xia ^{[2
,6
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, Dept Appl Math, Beijing 100083, Peoples R China

[2] UPMC Univ Paris 06, Sorbonne Univ, Lab Jacques Louis Lions, UMR 7598, 4 Pl Jussieu, F-75252 Paris, France

[3] ETH, ITS, Clausiusstr 47, CH-8092 Zurich, Switzerland

[4] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

[5] ETH, Inst Math Res ETH FIM, Ramistr 101, CH-8092 Zurich, Switzerland

[6] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2018年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Korteweg-de Vries equation; Resolvent estimation; Analytic semigroup; Gevrey class; STABILIZATION;

D O I：

10.1007/s11401-018-1060-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-dc Vries (KdV for short) equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup generated by the linear operator is not analytic but of Gevrey class delta is an element of(3/2, infinity) for t > 0.

引用

页码：201 / 212

页数：12

共 50 条

[41] Cylindrical nonlinear Schrodinger equation versus cylindrical Korteweg-de Vries equation
Fedele, Renato
De Nicola, Sergio
Grecu, Dan
Shukla, Padma K.
Visinescu, Anca
FRONTIERS IN MODERN PLASMA PHYSICS, 2008, 1061 : 273 - +
[42] Travelling wave solutions in a class of generalized Korteweg-de Vries equation
Shen, Jianwei
Xu, Wei
CHAOS SOLITONS & FRACTALS, 2007, 34 (04) : 1299 - 1306
[43] Asymptotic stability of a nonlinear Korteweg-de Vries equation with critical lengths
Chu, Jixun
Coron, Jean-Michel
Shang, Peipei
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (08) : 4045 - 4085
[44] Compacton Solutions of the Korteweg-de Vries Equation with Constrained Nonlinear Dispersion
Popov, S. P.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2019, 59 (01) : 150 - 159
[45] Integration of a loaded Korteweg-de Vries equation in a class of periodic functions
Yakhshimuratov A.B.
Matyokubov M.M.
Russian Mathematics, 2016, 60 (2) : 72 - 76
[46] New class of solutions of the Korteweg-de Vries-Burgers equation
Zayko, YN
Nefedov, IS
APPLIED MATHEMATICS LETTERS, 2001, 14 (01) : 115 - 121
[47] CONTROL OF A KORTEWEG-DE VRIES EQUATION: A TUTORIAL
Cerpa, Eduardo
MATHEMATICAL CONTROL AND RELATED FIELDS, 2014, 4 (01) : 45 - 99
[48] MSPRK Methods for the Korteweg-de Vries Equation
张凯
刘宏宇
张然
Northeastern Mathematical Journal, 2005, (04) : 387 - 390
[49] On the integrability of the octonionic Korteweg-de Vries equation
Restuccia, Alvaro
Sotomayor, Adrian
Veiro, Jean Pierre
XX CHILEAN PHYSICS SYMPOSIUM, 2018, 1043
[50] Bifurcations in the Generalized Korteweg-de Vries Equation
Kashchenko, S. A.
Preobrazhenskaya, M. M.
RUSSIAN MATHEMATICS, 2018, 62 (02) : 49 - 61

← 1 2 3 4 5 →