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On the Convergence of Hyperbolic Semigroups in Variable Hilbert Spaces

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Abstract

Resolvent convergence is considered for nonnegative self-adjoint operators acting in a variable Hilbert space Hε, with the limit of the resolvents being a pseudoresolvent. This convergence is used for passing to the limit in the corresponding hyperbolic operator equations in Hε viewed from the standpoint of semigroups. The scheme studied here can be applied to homogenization of nonstationary problems of elasticity for thin structures.

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  1. S. E. Pastukhova
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__________

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 24, pp. 215–249, 2004.

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Pastukhova, S.E. On the Convergence of Hyperbolic Semigroups in Variable Hilbert Spaces. J Math Sci 127, 2263–2283 (2005). https://doi.org/10.1007/s10958-005-0178-z

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  • DOI: https://doi.org/10.1007/s10958-005-0178-z

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