Abstract:
We prove an existence theorem for the statistical elasticity theory equation for a homogeneous incompressible medium and its extension to the second and third boundary value problem case. We demonstrate, in the case of the first, second, and third problems that, as λ→∞ the solution of the elasticity theory equation with Lam'e constants λ and μ converges to the solutions of the respective equations for incompressible material. An existence theorem in the rectangle is demonstrated for the third boundary value problem in W2q .
Citation:
G. M. Kobel'kov, “Concerning existence theorems for some problems of elasticity theory”, Mat. Zametki, 17:4 (1975), 599–609; Math. Notes, 17:4 (1975), 356–362
\Bibitem{Kob75}
\by G.~M.~Kobel'kov
\paper Concerning existence theorems for some problems of elasticity theory
\jour Mat. Zametki
\yr 1975
\vol 17
\issue 4
\pages 599--609
\mathnet{http://mi.mathnet.ru/mzm7579}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=399676}
\zmath{https://zbmath.org/?q=an:0365.73014|0338.35035}
\transl
\jour Math. Notes
\yr 1975
\vol 17
\issue 4
\pages 356--362
\crossref{https://doi.org/10.1007/BF01105388}
Linking options:
https://www.mathnet.ru/eng/mzm7579
https://www.mathnet.ru/eng/mzm/v17/i4/p599
This publication is cited in the following 4 articles:
G. M. Kobel'kov, “Symmetric approximations of the Navier–Stokes equations”, Sb. Math., 193:7 (2002), 1027–1047
G. M. Kobel'kov, “On the time-dependent Stokes problem”, Comput. Math. Math. Phys., 40:12 (2000), 1765–1768
M. A. Ol'shanskiǐ, “On a Stokes-type problem with a parameter”, Comput. Math. Math. Phys., 36:2 (1996), 193–202
Douglas N. Arnold, Richard S. Falk, “Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials”, Arch. Rational Mech. Anal., 98:2 (1987), 143