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21.
A model spectral problem of the form -i)y+xy= y on the finite interval [-1,1] with the Dirichlet boundary conditions is considered. Here is the spectral parameter and is positive. The behavior of the spectrum of this problem as 0 is completely investigated. The limit curves are found to which the eigenvalues concentrate and the counting eigenvalue functions along these curves are obtained. 相似文献
22.
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
23.
We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues
and eigenfunctions of the problems asm→−0.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999. 相似文献
24.
25.
N. N. Antonov I. A. Kolmakov V. V. Samartsev V. A. Shkalikov 《Journal of Applied Mechanics and Technical Physics》1989,30(6):857-862
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 30, No. 6, pp. 28–34, November–December, 1989. 相似文献
26.
Exponential Decay of Solution Energy for Equations Associated with Some Operator Models of Mechanics
We consider the equation
in a Hilbert space , where A is a uniformly positive self-adjoint operator and B is a dissipative operator. The main result is the proof of a theorem stating the exponential energy decay for solutions of this equation (or the exponential stability of the semigroup associated with the equation) under the additional assumption that B is sectorial and is subordinate to A in the sense of quadratic forms. 相似文献
27.
A. A. Shkalikov 《Journal of Mathematical Sciences》2004,124(6):5417-5441
The model problem -i y'+q(x)y= y, y(-1)=y(1)=0 is associated with the Orr-Sommerfeld operator well-known in hydrodynamics. Here is the spectral parameter, is the small parameter which is proportional to the viscosity of the liquid and to the reciprocal of the Reynolds number, and q(x) is the velocity of the stationary flow of the liquid in the channel |x| 1. We study the behavior of the spectrum of the corresponding model operator as to 0 with linear, quadratic, and monotonic analytic functions. We show that the sets of accumulation points of the spectra (the limit spectral graphs) of the model and corresponding Orr-Sommerfeld operators coincide just as the main terms of the eigenvalue counting functions along the curves of the graphs do. 相似文献
28.
Doklady Mathematics - The connection between the number of internal zeros of nontrivial solutions to fourth-order self-adjoint boundary value problems and the inertia index of these problems is... 相似文献
29.
A. E. Mihailov I. Z. Latypov A. A. Kalinkin A. V. Shkalikov A. A. Kalachev V. V. Samartsev 《Bulletin of the Russian Academy of Sciences: Physics》2011,75(12):1658-1663
Narrow-band orthogonally polarized collinear frequency-degenerate biphotons are generated in the process of the spontaneous
parametric down-conversion of light in a nonlinear BBO crystal placed in an optical resonator. Quantum polarization tomography
and polarization transformation of the generated biphoton states are performed. The results from our experiment agree well
with theoretical calculations. 相似文献
30.