Abstract
Two approaches are proposed for the modeling of deformation of elastic solids with small geometrical defects. The first approach is based on the theory of self adjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and the variational formulation is established. For both approaches the accuracy estimates are derived. Finally, the spectral problems are considered and the error estimates for eigenvalues are given.
Funding provided by grant from Institut franco-russe A.M. Liapunov d’informatique et de mathématiques appliquées
Partially supported by the grant 4 T11A 01524 of the State Committee for the Scientific Research of the Republic of Poland
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Nazarov, S.A., Sokolowski, J. (2005). Modeling of Topology Variations in Elasticity. In: Cagnol, J., Zolésio, JP. (eds) System Modeling and Optimization. CSMO 2003. IFIP International Federation for Information Processing, vol 166. Springer, Boston, MA. https://doi.org/10.1007/0-387-23467-5_9
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DOI: https://doi.org/10.1007/0-387-23467-5_9
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