Explicit solutions of boundary-value problems of thermoelasticity with microtemperatures for a half-space. (English. Russian original) Zbl 1351.35213
J. Math. Sci., New York 216, No. 4, 538-546 (2016); translation from Sovrem. Mat. Prilozh. 94 (2014).
Summary: We consider the statics case of the theory of linear thermoelasticity with microtemperatures materials. The representation formula of a general solution of the homogeneous system of differential equations obtained in this paper is expressed by means of four harmonic and three metaharmonic functions. These formulas are very convenient and useful in many particular problems for domains with concrete geometry. Here we demonstrare an application of these formulas to the III type boundary value problem for a half-space. Uniqueness theorems are proved. Solutions are obtained in quadratures.
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 35J57 | Boundary value problems for second-order elliptic systems |
| 74F05 | Thermal effects in solid mechanics |
| 74B10 | Linear elasticity with initial stresses |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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