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Stability of solutions for nonlinear wave equations with a positivenegative damping
1.  Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Siena, Via Roma 56, 53100 Siena 
2.  Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy 
References:
[1] 
A. Benaddi and B. Rao, Energy decay rate of wave equations with indefinite damping, J. Differential Equations, 161 (2000), 337357. 
[2] 
C. W. de Silva, "Vibration and Shock Handbook," Mechanical Engineering, CRC Press, 2005. doi: doi:10.1201/9781420039894. 
[3] 
G. Fragnelli and D. Mugnai, Stability of solutions for some classes of nonlinear damped wave equations, SIAM J. Control Optim., 47 (2008), 25202539. 
[4] 
P. Freitas and E. Zuazua, Stability results for the wave equation with indefinite damping, J. Differential Equations, 132 (1996), 338352. 
[5] 
A. Haraux, P. Martinez and J. Vancostenoble, Asymptotic stability for intermittently controlled second order evolution equations, SIAM J. Control and Opt., 43 (2005), 20892108. 
[6] 
L. Hatvani and T. Krisztin, Necessary and sufficient conditions for intermittent stabilization of linear oscillators by large damping, Differential Integral Equations, 10 (1997), 265272. 
[7] 
S. Konabe and T. Nikuni, Coarsegrained finitetemperature theory for the bose condensate in optical lattices, J. Low Temp. Phys., 150 (2008), 1246. doi: doi:10.1007/s1090900795174. 
[8] 
A. C. Lazer and P. J. McKenna, Largeamplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis, SIAM Review, 32 (1990), 537578. 
[9] 
H. A. Levine, S. R. Park and J. Serrin, Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation, J. Math. Anal. Appl., 228 (1998), 181205. 
[10] 
K. Liu, B. Rao and X. Zhang, Stabilization of the wave equations with potential and indefinite damping, J. Math. Anal. Appl., 269 (2002), 747769. 
[11] 
A. Marino and D. Mugnai, Asymptotically critical points and their multiplicity, Topol. Methods Nonlinear Anal., 19 (2002), 2938. 
[12] 
A. Marino and D. Mugnai, Asymptotical multiplicity and some reversed variational inequalities, Topol. Methods Nonlinear Anal., 20 (2002), 4362. 
[13] 
P. Martinez and J. Vancostenoble, Stabilization of the wave equation by onoff and positivenegative feedbacks, ESAIM Control Optim. Calc. Var., 7 (2002), 335377. 
[14] 
D. Mugnai, On a "reversed" variational inequality, Topol. Methods Nonlinear Anal., 17 (2001), 321358. 
[15] 
P. Pucci and J. Serrin, Asymptotic stability for intermittently controlled nonlinear oscillators, SIAM J. Math. Anal., 25 (1994), 815835. 
[16] 
P. Pucci and J. Serrin, Precise damping conditions for global asymptotic stability for nonlinear second order systems. II, J. Differential Equations, 113 (1994), 505534. 
[17] 
G. Somieski, Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods, Aerosp. Sci. Technol., 1 (1997), 545555. 
show all references
References:
[1] 
A. Benaddi and B. Rao, Energy decay rate of wave equations with indefinite damping, J. Differential Equations, 161 (2000), 337357. 
[2] 
C. W. de Silva, "Vibration and Shock Handbook," Mechanical Engineering, CRC Press, 2005. doi: doi:10.1201/9781420039894. 
[3] 
G. Fragnelli and D. Mugnai, Stability of solutions for some classes of nonlinear damped wave equations, SIAM J. Control Optim., 47 (2008), 25202539. 
[4] 
P. Freitas and E. Zuazua, Stability results for the wave equation with indefinite damping, J. Differential Equations, 132 (1996), 338352. 
[5] 
A. Haraux, P. Martinez and J. Vancostenoble, Asymptotic stability for intermittently controlled second order evolution equations, SIAM J. Control and Opt., 43 (2005), 20892108. 
[6] 
L. Hatvani and T. Krisztin, Necessary and sufficient conditions for intermittent stabilization of linear oscillators by large damping, Differential Integral Equations, 10 (1997), 265272. 
[7] 
S. Konabe and T. Nikuni, Coarsegrained finitetemperature theory for the bose condensate in optical lattices, J. Low Temp. Phys., 150 (2008), 1246. doi: doi:10.1007/s1090900795174. 
[8] 
A. C. Lazer and P. J. McKenna, Largeamplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis, SIAM Review, 32 (1990), 537578. 
[9] 
H. A. Levine, S. R. Park and J. Serrin, Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation, J. Math. Anal. Appl., 228 (1998), 181205. 
[10] 
K. Liu, B. Rao and X. Zhang, Stabilization of the wave equations with potential and indefinite damping, J. Math. Anal. Appl., 269 (2002), 747769. 
[11] 
A. Marino and D. Mugnai, Asymptotically critical points and their multiplicity, Topol. Methods Nonlinear Anal., 19 (2002), 2938. 
[12] 
A. Marino and D. Mugnai, Asymptotical multiplicity and some reversed variational inequalities, Topol. Methods Nonlinear Anal., 20 (2002), 4362. 
[13] 
P. Martinez and J. Vancostenoble, Stabilization of the wave equation by onoff and positivenegative feedbacks, ESAIM Control Optim. Calc. Var., 7 (2002), 335377. 
[14] 
D. Mugnai, On a "reversed" variational inequality, Topol. Methods Nonlinear Anal., 17 (2001), 321358. 
[15] 
P. Pucci and J. Serrin, Asymptotic stability for intermittently controlled nonlinear oscillators, SIAM J. Math. Anal., 25 (1994), 815835. 
[16] 
P. Pucci and J. Serrin, Precise damping conditions for global asymptotic stability for nonlinear second order systems. II, J. Differential Equations, 113 (1994), 505534. 
[17] 
G. Somieski, Shimmy analysis of a simple aircraft nose landing gear model using different mathematical methods, Aerosp. Sci. Technol., 1 (1997), 545555. 
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