Well-posedness and stability results for the Korteweg-de Vries-Burgers and Kuramoto-Sivashinsky equations with infinite memory: A history approach

被引：21

作者：

Chentouf, Boumediene ^{[1
]}

Guesmia, Aissa ^{[2
]}

机构：

[1] Kuwait Univ, Fac Sci, Dept Math, Safat 13060, Kuwait

[2] Univ Lorraine, Inst Elie Cartan Lorraine, UMR 7502, 3 Rue Augustin Fresnel,BP45112, F-57073 Metz, France

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2022年 / 65卷

关键词：

Korteweg-de Vries-Burgers equation; Kuramoto-Sivashinsky equation; Infinite memory; Well-posedness; Stability; Energy method; NONLINEAR BOUNDARY CONTROL; EXACT CONTROLLABILITY; NULL CONTROLLABILITY; DEVRIES EQUATION; PERIODIC DOMAIN; WAVE-EQUATION; STABILIZATION; SYSTEM; DECAY; STABILIZABILITY;

D O I：

10.1016/j.nonrwa.2022.103508

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main concern of the present paper is to study the well-posedness and stabilityproblem of two different dispersive systems subject to the effect of a distributedinfinite memory term. The two systems are respectively governed by the one-dimensional Korteweg-de Vries-Burgers and Kuramoto-Sivashinsky equations ina bounded domain[0,1]. In order to deal with the presence of the memory term,we adopt the history approach. First, we show that both problems are well-posedin appropriate functional spaces by means of the Fixed-Point Theorem providedthat the initial condition is sufficiently small. Then, the energy method enables usto provide a decay estimate of the systems' energy according to the assumptionssatisfied by the physical parameters and the memory kernel.(c) 2022 Elsevier Ltd. All rights reserved

引用

页数：30

共 46 条

[31] CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of the Burgers and Korteweg-de Vries-Burgers Equations [J].

Shapeev, Vasily P. ;

Vorozhtsov, Evgenii V. .

COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, CASC 2014, 2014, 8660 :432-446

[32] BOUNDARY CONTROL OF GENERALIZED KORTEWEG-DE VRIES-BURGERS-HUXLEY EQUATION: WELL-POSEDNESS, STABILIZATION AND NUMERICAL STUDIES [J].

Singh, Shri Lal Raghudev Ram ;

Mohan, Manil T. .

MATHEMATICAL CONTROL AND RELATED FIELDS, 2025, 15 (03) :1205-1240

[33] The well posedness of the dissipative Korteweg-de Vries equations with low regularity data [J].

Han, Jinsheng ;

Peng, Lizhong .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (01) :171-188

[34] Stability of a traveling-wave solution to the Cauchy problem for the Korteweg-de Vries-Burgers equation [J].

Kazeykina, A. V. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (04) :690-710

[35] Stability of a traveling-wave solution to the Cauchy problem for the Korteweg-de Vries-Burgers equation [J].

A. V. Kazeykina .

Computational Mathematics and Mathematical Physics, 2010, 50 :690-710

[36] Well-posedness and stability results for laminated Timoshenko beams with interfacial slip and infinite memory [J].

Guesmia, Aissa .

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2020, 37 (01) :300-350

[37] Well-posedness of Korteweg-de Vries-Benjamin Bona Mahony equation on a finite domain [J].

Li, Jie ;

Liu, Kangsheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 452 (01) :611-633

[38] Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces [J].

Boukarou, Aissa ;

Guerbati, Kaddour ;

Zennir, Khaled ;

Alodhaibi, Sultan ;

Alkhalaf, Salem .

MATHEMATICS, 2020, 8 (05)

[39] Convergence rate of solutions toward traveling waves for the Cauchy problem of generalized Korteweg-de Vries-Burgers equations [J].

Yin, Hui ;

Zhao, Huijiang ;

Zhou, Lina .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (09) :3981-3991

[40] Stability analysis of traveling wave solutions of a generalized Korteweg-de Vries-Burgers equation with variable dissipation parameter [J].

Shargatov, V. A. ;

Chugainova, A. P. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 397

← 1 2 3 4 5 →