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Griniv  R. O.  Shkalikov  A. A. 《Mathematical Notes》2003,73(5-6):618-624
In this paper, we consider equations of the form , where is a function with values in the Hilbert space , the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in . The linear operator generating the C 0-semigroup in the energy space is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms.  相似文献   
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Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 88, No. 1, pp. 7–13, July, 1991.  相似文献   
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This paper deals with the problem of small oscillations in a liquid layer of finite depth under the assumption that the bottom is an elastic medium. The system of equations corresponding to the problem is written out and explained. The main aim of the paper is to recast these equations in the form
(1)
, where and are positive operators in the function space naturally corresponding to the problem. The further aim is to investigate the spectrum of the linear pencil , which determines the dynamics of the problem. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 66–81, July, 2000.  相似文献   
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