Control and stability of the linearized dispersion-generalized Benjamin-Ono equation on a periodic domain

被引：0

作者：

Flores, C. ^{[1
]}

机构：

[1] Calif State Univ Channel Isl, One Univ Dr, Camarillo, CA 93012 USA

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2018年 / 30卷 / 03期

关键词：

Controllability; Stabilization; Linear KdV-like equations; Dispersive equations; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; DE-VRIES EQUATION; BOUNDARY CONTROLLABILITY; SCATTERING TRANSFORM; SOLITARY WAVES; STABILIZATION; STABILIZABILITY; KDV;

D O I：

10.1007/s00498-018-0219-z

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We investigate the exact control problem associated to the linearized dispersion-generalized Benjamin-Ono equation which contains fractional-order spatial derivatives on a periodic domain, T. More specifically, we establish that a mass-preserving external force can be applied to the linear system to achieve a final state from a given initial state. The stabilization problem with a linear feedback control is also studied.

引用

页数：16

共 48 条

[1] UNIQUENESS OF BENJAMIN SOLITARY-WAVE SOLUTION OF THE BENJAMIN-ONO-EQUATION [J].

AMICK, CJ ;

TOLAND, JF .

IMA JOURNAL OF APPLIED MATHEMATICS, 1991, 46 (1-2) :21-28

[2] INTERNAL WAVES OF PERMANENT FORM IN FLUIDS OF GREAT DEPTH [J].

BENJAMIN, TB .

JOURNAL OF FLUID MECHANICS, 1967, 29 :559-&

[3] INITIAL-VALUE PROBLEM FOR KORTEWEG-DEVRIES EQUATION [J].

BONA, JL ;

SMITH, R .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1975, 278 (1287) :555-601

[4]

Bourgain J., 1993, The KdV equations, GAGA, V3, P209, DOI 10.1007/BF01895688

[5] On well-posedness for the Benjamin-Ono equation [J].

Burq, Nicolas ;

Planchon, Fabrice .

MATHEMATISCHE ANNALEN, 2008, 340 (03) :497-542

[6] THE SCATTERING TRANSFORM FOR THE BENJAMIN-ONO-EQUATION [J].

COIFMAN, RR ;

WICKERHAUSER, MV .

INVERSE PROBLEMS, 1990, 6 (05) :825-861

[7] Sharp global well-posedness for KDV and modified KDV on R and T [J].

Colliander, J ;

Keel, M ;

Staffilani, G ;

Takaoka, H ;

Tao, T .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 16 (03) :705-749

[8] Stabilization and control for the nonlinear Schrodinger equation on a compact surface [J].

Dehman, B. ;

Gerard, P. ;

Lebeau, G. .

MATHEMATISCHE ZEITSCHRIFT, 2006, 254 (04) :729-749

[9]

Flores C, 2017, STABILIZATION DISPER

[10]

FOKAS AS, 1983, STUD APPL MATH, V68, P1

← 1 2 3 4 5 →