Basic Boundary-Value Problems for a Solid Body with Double Porosity and Two Nonintersecting Spherical Cavities

2015 ◽  
Vol 206 (4) ◽  
pp. 371-392
Author(s):  
L. Giorgashvili ◽  
G. Karseladze ◽  
M. Kharashvili
Keyword(s):  
Boundary Value Problems ◽  
Solid Body ◽  
Boundary Value ◽  
Double Porosity ◽  
Spherical Cavities ◽  
Basic Boundary

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.

scholarly journals Explicit Solutions of the Boundary Value Problems for an Ellipse with Double Porosity

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Lamara Bitsadze ◽  
Natela Zirakashvili
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Convergent Series ◽  
Double Porosity ◽  
Theory Of Elasticity ◽  
Classical Elasticity ◽  
Dimensional Boundary ◽  
Uniformly Convergent ◽  
Isotropic Bodies ◽  
Fully Coupled

The basic two-dimensional boundary value problems of the fully coupled linear equilibrium theory of elasticity for solids with double porosity structure are reduced to the solvability of two types of a problem. The first one is the BVPs for the equations of classical elasticity of isotropic bodies, and the other is the BVPs for the equations of pore and fissure fluid pressures. The solutions of these equations are presented by means of elementary (harmonic, metaharmonic, and biharmonic) functions. On the basis of the gained results, we constructed an explicit solution of some basic BVPs for an ellipse in the form of absolutely uniformly convergent series.

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