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Equivalence between observability and stabilization for a class of second order semilinear evolution
1.  Department of Mathematics, Florida International University, University Park, Miami, Florida 33199, United States 
[1] 
Louis Tebou. Wellposedness and stabilization of an EulerBernoulli equation with a localized nonlinear dissipation involving the $p$Laplacian. Discrete & Continuous Dynamical Systems  A, 2012, 32 (6) : 23152337. doi: 10.3934/dcds.2012.32.2315 
[2] 
Fathi Hassine. Asymptotic behavior of the transmission EulerBernoulli plate and wave equation with a localized KelvinVoigt damping. Discrete & Continuous Dynamical Systems  B, 2016, 21 (6) : 17571774. doi: 10.3934/dcdsb.2016021 
[3] 
Marcelo Moreira Cavalcanti. Existence and uniform decay for the EulerBernoulli viscoelastic equation with nonlocal boundary dissipation. Discrete & Continuous Dynamical Systems  A, 2002, 8 (3) : 675695. doi: 10.3934/dcds.2002.8.675 
[4] 
Yuri V. Rogovchenko, Fatoş Tuncay. Interval oscillation of a second order nonlinear differential equation with a damping term. Conference Publications, 2007, 2007 (Special) : 883891. doi: 10.3934/proc.2007.2007.883 
[5] 
Igor Chueshov, Irena Lasiecka, Daniel Toundykov. Longterm dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent. Discrete & Continuous Dynamical Systems  A, 2008, 20 (3) : 459509. doi: 10.3934/dcds.2008.20.459 
[6] 
Zhijian Yang, Zhiming Liu, Na Feng. Longtime behavior of the semilinear wave equation with gentle dissipation. Discrete & Continuous Dynamical Systems  A, 2016, 36 (11) : 65576580. doi: 10.3934/dcds.2016084 
[7] 
Kim Dang Phung. Boundary stabilization for the wave equation in a bounded cylindrical domain. Discrete & Continuous Dynamical Systems  A, 2008, 20 (4) : 10571093. doi: 10.3934/dcds.2008.20.1057 
[8] 
Kim Dang Phung. Decay of solutions of the wave equation with localized nonlinear damping and trapped rays. Mathematical Control & Related Fields, 2011, 1 (2) : 251265. doi: 10.3934/mcrf.2011.1.251 
[9] 
Aníbal RodríguezBernal, Enrique Zuazua. Parabolic singular limit of a wave equation with localized boundary damping. Discrete & Continuous Dynamical Systems  A, 1995, 1 (3) : 303346. doi: 10.3934/dcds.1995.1.303 
[10] 
Louis Tebou. Energy decay estimates for some weakly coupled EulerBernoulli and wave equations with indirect damping mechanisms. Mathematical Control & Related Fields, 2012, 2 (1) : 4560. doi: 10.3934/mcrf.2012.2.45 
[11] 
Jong Yeoul Park, Sun Hye Park. On uniform decay for the coupled EulerBernoulli viscoelastic system with boundary damping. Discrete & Continuous Dynamical Systems  A, 2005, 12 (3) : 425436. doi: 10.3934/dcds.2005.12.425 
[12] 
Maja Miletić, Dominik Stürzer, Anton Arnold. An EulerBernoulli beam with nonlinear damping and a nonlinear spring at the tip. Discrete & Continuous Dynamical Systems  B, 2015, 20 (9) : 30293055. doi: 10.3934/dcdsb.2015.20.3029 
[13] 
Joseph A. Iaia. Localized radial solutions to a semilinear elliptic equation in $\mathbb{R}^n$. Conference Publications, 1998, 1998 (Special) : 314326. doi: 10.3934/proc.1998.1998.314 
[14] 
Min Zhu. On the higherorder bfamily equation and Euler equations on the circle. Discrete & Continuous Dynamical Systems  A, 2014, 34 (7) : 30133024. doi: 10.3934/dcds.2014.34.3013 
[15] 
Alain Haraux, Mohamed Ali Jendoubi. Asymptotics for a second order differential equation with a linear, slowly timedecaying damping term. Evolution Equations & Control Theory, 2013, 2 (3) : 461470. doi: 10.3934/eect.2013.2.461 
[16] 
Jeong Ja Bae, Mitsuhiro Nakao. Existence problem for the Kirchhoff type wave equation with a localized weakly nonlinear dissipation in exterior domains. Discrete & Continuous Dynamical Systems  A, 2004, 11 (2&3) : 731743. doi: 10.3934/dcds.2004.11.731 
[17] 
JiannSheng Jiang, KungHwang Kuo, ChiKun Lin. Homogenization of second order equation with spatial dependent coefficient. Discrete & Continuous Dynamical Systems  A, 2005, 12 (2) : 303313. doi: 10.3934/dcds.2005.12.303 
[18] 
Jiayun Lin, Kenji Nishihara, Jian Zhai. Critical exponent for the semilinear wave equation with timedependent damping. Discrete & Continuous Dynamical Systems  A, 2012, 32 (12) : 43074320. doi: 10.3934/dcds.2012.32.4307 
[19] 
Imen Benabbas, Djamel Eddine Teniou. Observability of wave equation with Ventcel dynamic condition. Evolution Equations & Control Theory, 2018, 7 (4) : 545570. doi: 10.3934/eect.2018026 
[20] 
Gleb G. Doronin, Nikolai A. Larkin. Kawahara equation in a bounded domain. Discrete & Continuous Dynamical Systems  B, 2008, 10 (4) : 783799. doi: 10.3934/dcdsb.2008.10.783 
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