Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. I
-
R. Duduchava
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.
© 1995 Plenum Publishing Corporation
Articles in the same Issue
- The Boundary-Contact Problem of Elasticity for Homogeneous Anisotropic Media with a Contact on Some Part of the Boundaries
- Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. I
- Fractional Integrodifferentiation in Hölder Classes of Arbitrary Order
- Sequential Convergence in Topological Vector Spaces
- On Some Boundary Value Problems with Integral Conditions for Functional Differential Equations
- Construction of Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)
- Two-Dimension-Like Functions Defined on the Class of all Tychonoff Spaces
- The Cauchy–Nicoletti Problem with Poles
Articles in the same Issue
- The Boundary-Contact Problem of Elasticity for Homogeneous Anisotropic Media with a Contact on Some Part of the Boundaries
- Basic Boundary Value Problems of Thermoelasticity for Anisotropic Bodies with Cuts. I
- Fractional Integrodifferentiation in Hölder Classes of Arbitrary Order
- Sequential Convergence in Topological Vector Spaces
- On Some Boundary Value Problems with Integral Conditions for Functional Differential Equations
- Construction of Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)
- Two-Dimension-Like Functions Defined on the Class of all Tychonoff Spaces
- The Cauchy–Nicoletti Problem with Poles
