L. Jentsch; D, Natroshvili : Interaction between Thermoelastic and Scalar Oscillation Fields (general anisotropic case)

Author(s) :

L. Jentsch; D, Natroshvili

Title :

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

Electronic source :

[gzipped ps-file] 113 kB
[gzipped dvi-file] 51 kB

Preprint series

Technische Universität Chemnitz-Zwickau, Fakultät für Mathematik (Germany). Preprint 97-5, 1997

Published in :

Integral Equation and Operator Theory 28/1997; p.261-288,

Appeared in :

Integral Equation and Operator Theory 28/1997; p.261-288

Mathematics Subject Classification :

31B10 [ Integral representations of harmonic functions (higher-dimensional) ]

31B25 [ Boundary behavior of harmonic functions (higher-dim.) ]

35C15 [ Integral representations of solutions of PDE ]

35E05 [ Fundamental solutions (PDE with constant coefficients) ]

45F15 [ Systems of singular linear integral equations ]

73B30 [ Thermodynamics of solids ]

73B40 [ Anisotropic materials ]

73C15 [ Uniqueness theorems in elasticity ]

73D30 [ Linear vibrations of solids ]

Abstract :

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.

Keywords :

Fluid-solid interaction, anisotropic bodies, boundary integral method

Language :

english

Publication time :

2/1997