Asymptotic distribution of the eigenvalues and eigenfunctions in basic boundary value oscillation problems in hemitropic elasticity

2013 ◽  
Vol 53 (7) ◽  
pp. 984-999
Author(s):  
Yu. A. Bezhuashvili ◽  
R. V. Rukhadze
Keyword(s):  
Asymptotic Distribution ◽  
Boundary Value ◽  
Eigenvalues And Eigenfunctions ◽  
Basic Boundary

scholarly journals ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND EIGENFUNCTIONS OF A NONLOCAL BOUNDARY VALUE PROBLEM

2021 ◽  
Vol 26 (2) ◽  
pp. 253-266
Author(s):  
Erdoğan Şen ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Asymptotic Distribution ◽  
Nonlocal Boundary Condition ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Asymptotic Formulas ◽  
Nonlocal Boundary Value Problem ◽  
Eigenvalues And Eigenfunctions ◽  
Distribution Of Eigenvalues

In this work, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the second order boundary-value problem with a Bitsadze–Samarskii type nonlocal boundary condition.

Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. I

1995 ◽  
Vol 2 (2) ◽  
pp. 123-140
Author(s):  
R. Duduchava ◽  
D. Natroshvili ◽  
E. Shargorodsky
Keyword(s):  
Boundary Value Problems ◽  
Displacement Vector ◽  
Boundary Value ◽  
Three Dimensional ◽  
Manifolds With Boundary ◽  
Hölder Continuous ◽  
Arbitrary Configuration ◽  
Anisotropic Bodies ◽  
Potential Methods ◽  
Basic Boundary

Abstract The three-dimensional problems of the mathematical theory of thermoelasticity are considered for homogeneous anisotropic bodies with cuts. It is assumed that the two-dimensional surface of a cut is a smooth manifold of an arbitrary configuration with a smooth boundary. The existence and uniqueness theorems for boundary value problems of statics and pseudo-oscillations are proved in the Besov and Bessel-potential spaces by means of the classical potential methods and the theory of pseudodifferential equations on manifolds with boundary. Using the embedding theorems, it is proved that the solutions of the considered problems are Hölder continuous. It is shown that the displacement vector and the temperature distribution function are Cα -regular with any exponent α < 1/2. This paper consists of two parts. In this part all the principal results are formulated. The forthcoming second part will deal with the auxiliary results and proofs.

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