STABILITY OF SOLUTIONS FOR NONLINEAR WAVE EQUATIONS WITH A POSITIVE NEGATIVE DAMPING

被引：9

作者：

Fragnelli, Genni ^{[1
]}

Mugnai, Dimitri ^{[2
]}

机构：

[1] Univ Siena, Dipartimento Ingn Informaz, Via Roma 56, I-53100 Siena, Italy

[2] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2011年 / 4卷 / 03期

关键词：

Damped nonlinear wave equations; positive-negative damping;

D O I：

10.3934/dcdss.2011.4.615

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a stability result for damped nonlinear wave equations, when the damping changes sign and the nonlinear term satisfies a few natural assumptions.

引用

页码：615 / 622

页数：8

共 17 条

[1] Energy decay rate of wave equations with indefinite damping [J].

Benaddi, A ;

Rao, BP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 161 (02) :337-357

[2] STABILITY OF SOLUTIONS FOR SOME CLASSES OF NONLINEAR DAMPED WAVE EQUATIONS [J].

Fragnelli, Genni ;

Mugnai, Dimitri .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2008, 47 (05) :2520-2539

[3] Stability results for the wave equation with indefinite damping [J].

Freitas, P ;

Zuazua, E .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 132 (02) :338-352

[4] Asymptotic stability for intermittently controlled second-order evolution equations [J].

Haraux, A ;

Martinez, P ;

Vancostenoble, J .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2005, 43 (06) :2089-2108

[5]

Hatvani L., 1997, DIFFERENTIAL INTEGRA, V10, P265

[6] Coarse-grained finite-temperature theory for the bose condensate in optical lattices [J].

Konabe, S. ;

Nikuni, T. .

JOURNAL OF LOW TEMPERATURE PHYSICS, 2008, 150 (1-2) :12-46

[7] LARGE-AMPLITUDE PERIODIC OSCILLATIONS IN SUSPENSION BRIDGES - SOME NEW CONNECTIONS WITH NONLINEAR-ANALYSIS [J].

LAZER, AC ;

MCKENNA, PJ .

SIAM REVIEW, 1990, 32 (04) :537-578

[8] Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation [J].

Levine, HA ;

Park, SR ;

Serrin, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 228 (01) :181-205

[9]

Lin J.H., 2005, Vibration and Shock Handbook

[10] Stabilization of the wave equations with potential and indefinite damping [J].

Liu, KS ;

Rao, BP ;

Zhang, X .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 269 (02) :747-769

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