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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-199801162 |
| Date | 30 October 1998 |
| Creators | Jentsch, L., Natroshvili, D |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, application/postscript, application/x-dvi, text/plain, application/zip |
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