The basic boundary value problems of static elasticity theory and their Cosserat spectrum
type: Item
instance of: scholarly article
title: The basic boundary value problems of static elasticity theory and their Cosserat spectrum
zbMATH Open document ID: 0793.73021
DOI: 10.1007/BF03025721
author: Alexander Kozhevnikov
published in: Mathematische Zeitschrift
publication date: 1994-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/174529
review text: The well-known Liechtenstein's method [\textit{L. Liechtenstein}, Math. Z. 20, 21-28 (1924)] of reducing the first basic boundary problem of static elasticity theory (BPET) to equivalent integral Fredholm equation of the second kind on the boundary is extended to all the rest BPET (the second, third and fourth). The Cosserat spectra of all four BPET's are also studied, and the asymptotics of finite-multiple eigenvalues tending to a unique limiting point \(-2\), 0, \(-1\) or \(-1\) are obtained for the first, second, third or fourth BPET, respectively. For the Stokes problem from hydromechanics (linearized stationary Navier- Stokes equation), we prove the convergence in Sobolev space of a new iteration algorithm for construction of the solution; this algorithm is much better than the known algorithm by Uzawa and Arrow-Hurwicz.
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 549771
zbMATH Keywords: Liechtenstein's method
zbMATH Keywords: Fredholm equation of the second kind
zbMATH Keywords: asymptotics
zbMATH Keywords: eigenvalues
zbMATH Keywords: convergence
zbMATH Keywords: Sobolev space
zbMATH Keywords: iteration
MaRDI profile type: Publication
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OpenAlex ID: W2057690939
description: scientific article; zbMATH DE number 549771