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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Mixed Interface Problems of Thermoelastic Pseudo-Oscillations

Jentsch, L., Natroshvili, D., Sigua, I. 30 October 1998 (has links) (PDF)
Three-dimensional basic and mixed interface problems of the mathematical theory of thermoelastic pseudo-oscillations are considered for piecewise homogeneous anisotropic bodies. Applying the method of boundary potentials and the theory of pseudodifferential equations existence and uniqueness theorems of solutions are proved in the space of regular functions C^(k+ alpha) and in the Bessel-potential (H^(s)_(p)) and Besov (B^(s)_(p,q)) spaces. In addition to the classical regularity results for solutions to the basic interface problems, it is shown that in the mixed interface problems the displacement vector and the temperature are Hölder continuous with exponent 0<alpha<1/2.
2

Interaction between Thermoelastic and Scalar Oscillation Fields (general anisotropic case)

Jentsch, L., Natroshvili, D 30 October 1998 (has links) (PDF)
Three-dimensional mathematical problems of the interaction between thermoelastic and scalar oscillation fields are considered in a general anisotropic case. An elastic structure is assumed to be a bounded homogeneous anisortopic body occupying domain $\Omega^+\sub\R^3$ , where the thermoelastic field is defined, while in the physically anisotropic unbounded exterior domain $\Omega^-=\R^3\\ \overline{\Omega^+}$ there is defined the scalar field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface $\delta\Omega^{+-}$. Uniqueness and existence theorems, for the non-resonance case, are proved by the reduction of the original interface problems to equivalent systems of boundary pseudodifferential equations ($\Psi DEs$) . The invertibility of the corresponding matrix pseudodifferential operators ($\Psi DO$) in appropriate functional spaces is shown on the basis of generalized Sommerfeld-Kupradze type thermoradiation conditions for anisotropic bodies. In the resonance case, the co-kernels of the $\Psi DOs$ are analysed and the efficent conditions of solvability of the transmission problems are established.
3

Thermoelastic Oscillations of Anisotropic Bodies

Jentsch, L., Natroshvili, D. 30 October 1998 (has links) (PDF)
The generalized radiation conditions at infinity of Sommerfeld-Kupradze type are established in the theory of thermoelasticity of anisotropic bodies. Applying the potential method and the theory of pseudodifferential equations on manifolds the uniqueness and existence theorems of solutions to the basic three-dimensional exterior boundary value problems are proved and representation formulas of solutions by potential type integrals are obtained.
4

Three-dimensional mathematical Problems of thermoelasticity of anisotropic Bodies

Jentsch, Lothar, Natroshvili, David 30 October 1998 (has links) (PDF)
CHAPTER I. Basic Equations. Fundamental Matrices. Thermo-Radiation Conditions 1. Basic differential equations of thermoelasticity theory 2. Fundamental matrices 3. Thermo-radiating conditions. Somigliana type integral representations CHAPTER II. Formulation of Boundary Value and Interface Problems 4. Functional spaces 5. Formulation of basic and mixed BVPs 6. Formulation of crack type problems 7. Formulation of basic and mixed interface problems CHAPTER III. Uniqueness Theorems 8. Uniqueness theorems in pseudo-oscillation problems 9. Uniqueness theorems in steady state oscillation problems CHAPTER IV. Potentials and Boundary Integral Operators 10. Thermoelastic steady state oscillation potentials 11. Pseudo-oscillation potentials CHAPTER V. Regular Boundary Value and Interface Problems 12. Basic BVPs of pseudo-oscillations 13. Basic exterior BVPs of steady state oscillations 14. Basic interface problems of pseudo-oscillations 15. Basic interface problems of steady state oscillations CHAPTER VI. Mixed and Crack Type Problems 16. Basic mixed BVPs 17. Crack type problems 18. Mixed interface problems of steady state oscillations 19. Mixed interface problems of pseudo-oscillations
5

Thermoelastic Oscillations of Anisotropic Bodies

Jentsch, L., Natroshvili, D. 30 October 1998 (has links)
The generalized radiation conditions at infinity of Sommerfeld-Kupradze type are established in the theory of thermoelasticity of anisotropic bodies. Applying the potential method and the theory of pseudodifferential equations on manifolds the uniqueness and existence theorems of solutions to the basic three-dimensional exterior boundary value problems are proved and representation formulas of solutions by potential type integrals are obtained.
6

Mixed Interface Problems of Thermoelastic Pseudo-Oscillations

Jentsch, L., Natroshvili, D., Sigua, I. 30 October 1998 (has links)
Three-dimensional basic and mixed interface problems of the mathematical theory of thermoelastic pseudo-oscillations are considered for piecewise homogeneous anisotropic bodies. Applying the method of boundary potentials and the theory of pseudodifferential equations existence and uniqueness theorems of solutions are proved in the space of regular functions C^(k+ alpha) and in the Bessel-potential (H^(s)_(p)) and Besov (B^(s)_(p,q)) spaces. In addition to the classical regularity results for solutions to the basic interface problems, it is shown that in the mixed interface problems the displacement vector and the temperature are Hölder continuous with exponent 0<alpha<1/2.
7

Interaction between Thermoelastic and Scalar Oscillation Fields (general anisotropic case)

Jentsch, L., Natroshvili, D 30 October 1998 (has links)
Three-dimensional mathematical problems of the interaction between thermoelastic and scalar oscillation fields are considered in a general anisotropic case. An elastic structure is assumed to be a bounded homogeneous anisortopic body occupying domain $\Omega^+\sub\R^3$ , where the thermoelastic field is defined, while in the physically anisotropic unbounded exterior domain $\Omega^-=\R^3\\ \overline{\Omega^+}$ there is defined the scalar field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface $\delta\Omega^{+-}$. Uniqueness and existence theorems, for the non-resonance case, are proved by the reduction of the original interface problems to equivalent systems of boundary pseudodifferential equations ($\Psi DEs$) . The invertibility of the corresponding matrix pseudodifferential operators ($\Psi DO$) in appropriate functional spaces is shown on the basis of generalized Sommerfeld-Kupradze type thermoradiation conditions for anisotropic bodies. In the resonance case, the co-kernels of the $\Psi DOs$ are analysed and the efficent conditions of solvability of the transmission problems are established.
8

Three-dimensional mathematical Problems of thermoelasticity of anisotropic Bodies

Jentsch, Lothar, Natroshvili, David 30 October 1998 (has links)
CHAPTER I. Basic Equations. Fundamental Matrices. Thermo-Radiation Conditions 1. Basic differential equations of thermoelasticity theory 2. Fundamental matrices 3. Thermo-radiating conditions. Somigliana type integral representations CHAPTER II. Formulation of Boundary Value and Interface Problems 4. Functional spaces 5. Formulation of basic and mixed BVPs 6. Formulation of crack type problems 7. Formulation of basic and mixed interface problems CHAPTER III. Uniqueness Theorems 8. Uniqueness theorems in pseudo-oscillation problems 9. Uniqueness theorems in steady state oscillation problems CHAPTER IV. Potentials and Boundary Integral Operators 10. Thermoelastic steady state oscillation potentials 11. Pseudo-oscillation potentials CHAPTER V. Regular Boundary Value and Interface Problems 12. Basic BVPs of pseudo-oscillations 13. Basic exterior BVPs of steady state oscillations 14. Basic interface problems of pseudo-oscillations 15. Basic interface problems of steady state oscillations CHAPTER VI. Mixed and Crack Type Problems 16. Basic mixed BVPs 17. Crack type problems 18. Mixed interface problems of steady state oscillations 19. Mixed interface problems of pseudo-oscillations

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