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Asymptotic modeling of the problem with contrasting stiffness

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An asymptotic model is found for the Neumann problem for the second-order differential equation with piecewise constant coefficients in a composite domain Ω∪ω, which are small, of order ε, in the subdomain ω. Namely, a domain Ω(ε) with a singular perturbed boundary is constructed, the solution for which provides a two-term asymptotic, that is, of increased accuracy O(ε2| log ε|3/2), approximation to the restriction to Ω of the solution of the original problem. As opposed to other singularly perturbed problems, in the case of contrasting stiffness, the modeling requires the construction of a contour ∂Ω(ε) with ledges, i.e., with boundary fragments of curvature O(ε−1). Bibliography: 33 titles.

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  1. Institute of Problems in Mechanical Engineering, RAS, St. Petersburg, Russia

    S. A. Nazarov

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  1. S. A. Nazarov
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Correspondence to S. A. Nazarov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 369, 2009, pp. 164–201.

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Nazarov, S.A. Asymptotic modeling of the problem with contrasting stiffness. J Math Sci 167, 692–712 (2010). https://doi.org/10.1007/s10958-010-9955-4

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