On the spectrum of Euler–Bernoulli beam equation with Kelvin–Voigt damping☆

[1]  George D. Birkhoff,et al.  On the asymptotic character of the solutions of certain linear differential equations containing a parameter , 1908 .

[2]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[3]  F. Smithies Linear Operators , 2019, Nature.

[4]  P. Goldbart,et al.  Linear differential operators , 1967 .

[5]  P. Zweifel Advanced Mathematical Methods for Scientists and Engineers , 1980 .

[6]  J. Lagnese,et al.  Control of Wave Processes with Distributed Controls Supported on a Subregion , 1983 .

[7]  A. Haraux,et al.  Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire , 1989 .

[8]  Exact controllability of the one-dimensional wave equation with locally distributed control , 1990 .

[9]  Stéphane Jaffard Contrôle interne exact des vibrations d'une plaque rectangulaire , 1990 .

[10]  M. A. Kaashoek,et al.  Classes of Linear Operators Vol. I , 1990 .

[11]  Enrique Zuazua,et al.  Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping , 1990 .

[12]  I. Gohberg,et al.  Classes of Linear Operators , 1990 .

[13]  F. J. Narcowich,et al.  Exponential decay of energy of evolution equations with locally distributed damping , 1991 .

[14]  Mauro Fabrizio,et al.  On the existence and the asymptotic stability of solutions for linearly viscoelastic solids , 1991 .

[15]  V. Komornik On the exact internal controllability of a Petrowsky system , 1992 .

[16]  Kazufumi Ito,et al.  Well posedness for damped second-order systems with unbounded input operators , 1995, Differential and Integral Equations.

[17]  E. Zuazua,et al.  Stability Results for the Wave Equation with Indefinite Damping , 1996 .

[18]  On the type ofCo-semigroup associated with the abstract linear viscoelastic system , 1996 .

[19]  Zhuangyi Liu,et al.  Analyticity and Differentiability of Semigroups Associated with Elastic Systems with Damping and Gyroscopic Forces , 1997 .

[20]  Kangsheng Liu Locally Distributed Control and Damping for the Conservative Systems , 1997 .

[21]  Harvey Thomas Banks,et al.  Experimental Confirmation of a PDE-Based Approach to Design of Feedback Controls , 1997 .

[22]  Qi Zhou,et al.  Exact internal controllability of Maxwell’s equations , 1997 .

[23]  Kangsheng Liu,et al.  Exponential Decay of Energy of the Euler--Bernoulli Beam with Locally Distributed Kelvin--Voigt Damping , 1998 .

[24]  Kangsheng Liu,et al.  Spectrum and Stability for Elastic Systems with Global or Local Kelvin-Voigt Damping , 1998, SIAM J. Appl. Math..

[25]  K. Gu Stability and Stabilization of Infinite Dimensional Systems with Applications , 1999 .

[26]  Bopeng Rao,et al.  Energy Decay Rate of Wave Equations with Indefinite Damping , 2000 .

[27]  Riesz spectral systems , 2001 .

[28]  Kangsheng Liu,et al.  Exponential Stability of an Abstract Nondissipative Linear System , 2001, SIAM J. Control. Optim..

[29]  Bao-Zhu Guo,et al.  Riesz Basis Approach to the Stabilization of a Flexible Beam with a Tip Mass , 2000, SIAM J. Control. Optim..

[30]  Zhuangyi Liu,et al.  Exponential decay of energy of vibrating strings with local viscoelasticity , 2002 .

[31]  Bao-Zhu Guo,et al.  Riesz Basis Property and Exponential Stability of Controlled Euler--Bernoulli Beam Equations with Variable Coefficients , 2001, SIAM J. Control. Optim..

[32]  Jacob T. Schwartz,et al.  Linear operators. Part II. Spectral theory , 2003 .

[33]  M. Renardy On localized Kelvin‐Voigt damping , 2004 .

[34]  Stabilité exponentielle des équations des ondes avec amortissement local de Kelvin–Voigt , 2004 .

[35]  A Note on the Exponential Decay of Energy of a Euler–Bernoulli Beam with Local Viscoelasticity , 2004 .

[36]  Kangsheng Liu,et al.  Stability for the Timoshenko Beam System with Local Kelvin–Voigt Damping , 2005 .

[37]  Bao-Zhu Guo,et al.  BOUNDARY FEEDBACK STABILIZATION OF A THREE-LAYER SANDWICH BEAM: RIESZ BASIS APPROACH ∗ , 2006 .

[38]  B. Rao,et al.  Exponential stability for the wave equations with local Kelvin–Voigt damping , 2006 .

[39]  B. Jacob,et al.  Location of the spectrum of operator matrices which are associated to second order equations , 2007 .

[40]  G. Xu,et al.  Spectrum of an operator arising elastic system with local K‐V damping , 2008 .

[41]  Carsten Trunk,et al.  Analyticity and Riesz basis property of semigroups associated to damped vibrations , 2008 .

[42]  B. Guo,et al.  Spectral analysis of a wave equation with Kelvin‐Voigt damping , 2010 .