A QUADRATIC EIGENVALUE PROBLEM INVOLVING STOKES EQUATIONS

被引:12
作者
CONCA, C
DURAN, M
PLANCHARD, J
机构
[1] ELECT FRANCE,DEPT MMN,DIRECT ETUD & RECH,1 AVE DU GEN DE GAULLE,F-92141 CLAMART,FRANCE
[2] UNIV CHILE,FAC CIENCIAS FIS & MATEMAT,DEPT INGN MATEMAT,SANTIAGO,CHILE
关键词
D O I
10.1016/0045-7825(92)90086-Y
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
An existence theorem for the eigenvalues of a spectral problem is studied in this paper. The physical situation behind this mathematical problem is the determination of the eigenfrequencies and eigenmotions of a fluid-solid structure. The liquid part in this structure is represented by a viscous incompressible fluid, while the solid part is a set of parallel rigid tubes. The spectral problem governing this system is a quadratic eigenvalue problem which involves Stokes equations with a non-local boundary condition. The strategy for tackling the question of existence of eigenvalues consists of proving that the original problem is equivalent to that of determining the characteristic values of a linear (non-selfadjoint) compact operator. Sharp estimates for the eigenvalues give precise information about the region of C where the eigenvalues are located. In particular, we prove that this problem admits a countable set of eigenvalues in which only a finite number of them have a non-zero imaginary part.
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页码:295 / 313
页数:19
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