Within the framework of the uncoupled thermoelasticity, using G. Weyl’s method, asymptotic formulas for eigenvalues and eigenfunctions of the first boundary-value problem have been obtained for cubically anisotropic bodies limited by a finite number of closed and nonclosed unintersecting Lyapunov surfaces.
Similar content being viewed by others
References
Yu. M. Kolyano, Methods of Determining the Thermal Conductivity and Thermoelasticity of an Inhomogeneous Body [in Russian], Naukova Dumka, Kiev (1992).
Ya. B. Lopatinskii, The Theory of General Boundary Problem. Selected Papers [in Russian], Naukova Dumka, Kiev (1984).
Mar. D. Martynenko, Some boundary-value problems for elliptic systems, Dokl. Akad. Nauk USSR, Ser. A, No. 8, 699–702 (1968).
V. I. Smirnov, A Course of Higher Mathematics [in Russian], Vol. 4, Pt. 2, Nauka, Moscow (1981).
A. B. Drapkin, The asymptotics of eigenvalues and functions of the Dirichlet-type problems for a single class of elliptic systems, Naukovi Zap. L’viv Univ., Issue 8, 134–147 (1957).
H. Weyl, Selected Papers. Mathematics, Theoretical Physics [Russian translation], Nauka, Moscow (1984).
Author information
Authors and Affiliations
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 1010–1015, September–October, 2008.
Rights and permissions
About this article
Cite this article
Martynenko, I.M. Asymptotics of the eigenvalues and eigenfunctions in cubically anisotropic thermoelastic bodies with slits. J Eng Phys Thermophy 81, 1055–1060 (2008). https://doi.org/10.1007/s10891-009-0107-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-009-0107-y