Vibrating systems with heavy soft inclusions (in Ukrainian)

Author V. M. Hut
Ivan Franko National University of Lviv

Abstract The Neumann spectral problem for an elliptic operator of the second order with singularly perturbed coefficients is considered. The asymptotic behavior of eigenvalues and eigenfunctions is studied. The problem describes the eigenmodes of a composite material with a finite number of heavy and soft inclusions. The number-by-number convergence of the eigenvalues and the corresponding eigenspaces is established. The limit eigenvalue problem involves a non-local boundary condition which arises from the non trivial coupling of the inclusions.
Keywords spectral Neumann problem; eigenvalue; eigenfunction; singular perturbation; asymptotics of spectrum; heavy inclusions
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Pages 162-176
Volume 38
Issue 2
Year 2012
Journal Matematychni Studii
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