1 |
Massatt P . Limiting behavior for strongly damped nonlinear wave equations. J Differ Equ, 1983, 48 (3): 334- 349
doi: 10.1016/0022-0396(83)90098-0
|
2 |
Huang F L . On the mathematical model for linear elastic systems with analytic damping. SIAM J Control Optim, 1988, 26 (3): 714- 724
doi: 10.1137/0326041
|
3 |
Griniv R O , Shkalikov A A . Exponential stability of semigroups related to operator models in mechanics. Math Notes, 2003, 73 (5): 618- 624
|
4 |
Weiss G , Tucsnak M . How to get a conservative well-posed linear system out of thin air. Part Ⅱ. Controllability and stability. SIAM J Control Optim, 2003, 42 (3): 907- 935
doi: 10.1137/S0363012901399295
|
5 |
Bátkai A , Engel K J . Exponential decay of 2 × 2 operator matrix semigroups. J Comput Anal Appl, 2004, 6 (2): 153- 163
|
6 |
邱汶汶, 齐雅茹. 一类无界算子的二次数值域和谱. 数学物理学报, 2020, 40A (6): 1420- 1430
doi: 10.3969/j.issn.1003-3998.2020.06.002
|
|
Qiu W W , Qi Y R . The quadratic numerical range and the spectrum of some unbounded block operator matrices. Acta Math Sci, 2020, 40A (6): 1420- 1430
doi: 10.3969/j.issn.1003-3998.2020.06.002
|
7 |
Jacob B , Trunk C . Location of the spectrum of operator matrices which are associated to second order equations. Oper Matrices, 2007, 1 (1): 45- 60
|
8 |
Jacob B , Trunk C , Winklmeier M . Analyticity and riesz basis property of semigroups associated to damped vibrations. J Evol Equ, 2008, 8 (2): 263- 281
doi: 10.1007/s00028-007-0351-6
|
9 |
Jacob B , Trunk C . Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics. Semigroup Forum, 2009, 79 (1): 79- 100
doi: 10.1007/s00233-009-9148-y
|
10 |
Artamonov N V . Estimate of the decay exponent of an operator semigroup associated with a second-order linear differential equation. Math Notes, 2012, 91 (5/6): 731- 734
|
11 |
Jacob B , Langer M , Tretter C . Variational principles for self-adjoint operator functions arising from second order systems. Oper Matrices, 2016, 10 (3): 501- 531
|
12 |
Jacob B , Tretter C , Trunk C , Vogt H . Systems with strong damping and their spectra. Math Methods Appl Sci, 2018, 41 (16): 6546- 6573
doi: 10.1002/mma.5166
|
13 |
Huang F L . Some problems for linear elastic systems with damping. Acta Math Sci, 1990, 10 (3): 319- 326
doi: 10.1016/S0252-9602(18)30405-3
|
14 |
Mugnolo D. A variational approach to strongly damped wave equations//Amann W, Arendt M, Hieber I, Neubrander FM, Nicaise S, eds. Functional Analysis and Evolution Equations: The Günter Lumer Volume. Basel: Birkhäuser, 2008: 503-514
|
15 |
Francesca B . A dirichlet boundary contral problem for the strongly damped wave equation. SIAM J Control Optim, 1992, 30 (5): 1092- 1100
doi: 10.1137/0330058
|
16 |
Chen S P , Liu K S , Liu Z Y . Spectrum and stability for elastic systems with global or local Kelvin-Voigt damping. SIAM J Appl Math, 1998, 50 (2): 651- 668
|
17 |
Lasiecka I , Pandolfi L , Triggiani R . A singular control approach to highly damped second-order abstract equations and applications. Appl Math Optim, 1997, 36, 67- 107
|
18 |
Weidmann J . Linear Operators in Hilbert Spaces. New York: Springer-Verlag, 1980
|
19 |
Bognar J . Indefinite Inner Product Spaces. New York: Springer-Verlag, 1974
|
20 |
吴德玉, 阿拉坦仓. 分块算子矩阵谱理论及其应用. 北京: 科学出版社, 2013
|
|
Wu D Y , Alatancang . The Spectral Theory of Block Operator Matrices and Its Applications. Beijing: Science Press, 2013
|
21 |
Kato T . Perturbation Theory for Linear Operators. Berlin: Springer-Verlag, 1976
|
22 |
Hundertmark D , Lee Y R . Exponential decay of eigenfunctions and generalized eigenfunctions of a non-self-adjoint matrix Schrödinger operator related to NLS. Bull London Math Soc, 2007, 39 (5): 709- 720
doi: 10.1112/blms/bdm065
|
23 |
Azizov T Y , Jonas P , Trunk C . Spectral points of type π+ and π- of self-adjoint operators in Krein spaces. J Funct Anal, 2005, 226, 114- 137
doi: 10.1016/j.jfa.2005.03.009
|