Stabilization of solutions of dissipative Hamiltonian systems

被引：1

作者：

Chill, Ralph ^{[1
,2
]}

Radzki, Wiktor ^{[3
,4
]}

机构：

[1] Univ Paul Verlaine Metz, F-57045 Metz 1, France

[2] CNRS, Lab Math & Applicat Metz, UMR 7122, F-57045 Metz 1, France

[3] Nicholas Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

[4] W Pomeranian Univ Technol, Sch Math, PL-70310 Szczecin, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 380卷 / 02期

关键词：

Damped Hamiltonian system; Convergence to equilibrium; Lojasiewicz inequality; Spherical pendulum; Henon-Heiles system; CONVERGENCE; EQUATIONS;

D O I：

10.1016/j.jmaa.2011.02.077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the stabilization of solutions of damped Hamiltonian systems. We give sufficient conditions for convergence of these solutions, decay estimate and examples of applications. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：750 / 758

页数：9

共 11 条

[1] Convergence of the iterates of descent methods for analytic cost functions [J].

Absil, PA ;

Mahony, R ;

Andrews, B .

SIAM JOURNAL ON OPTIMIZATION, 2005, 16 (02) :531-547

[2]

Arnol'd V. I., 1988, ENCY MATH SCI, V3

[3] APPLICATIONS OF THE LOJASIEWICZ-SIMON GRADIENT INEQUALITY TO GRADIENT-LIKE EVOLUTION EQUATIONS [J].

Chill, Ralph ;

Haraux, Alain ;

Jendoubi, Mohamed Ali .

ANALYSIS AND APPLICATIONS, 2009, 7 (04) :351-372

[4]

CURRY HB, 1944, Q APPL MATH, V2

[5]

GALLOT S., 2004, Riemannian Geometry., V3rd

[6] APPLICABILITY OF 3 INTEGRAL OF MOTION - SOME NUMERICAL EXPERIMENTS [J].

HENON, M ;

HEILES, C .

ASTRONOMICAL JOURNAL, 1964, 69 (01) :73-&

[7] Non-stabilizing solutions of semilinear hyperbolic and elliptic equations with damping [J].

Jendoubi, MA ;

Polácik, P .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2003, 133 :1137-1153

[8] Pointwise convergence of gradient-like systems [J].

Lageman, Christian .

MATHEMATISCHE NACHRICHTEN, 2007, 280 (13-14) :1543-1558

[9]

LOJASIEWICZ S, 1963, Les equations aux derivees partielles, P87

[10]

Lojasiewicz S., 1965, ENSEMBLES SEMIANALYT

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