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**Non-stationary problems of generalized elastothermodiffusion for inhomogeneous media.**
*(English)*
Zbl 0806.73005

The Green-Lindsay theory is generalized to problems of elastothermodiffusion. Initial-boundary value problems are investigated for the considered physical system of differential equations in piecewise-homogeneous media with boundary and contact conditions; a substantiation of the Riesz-Fischer-Kupradze method is given, and approximate solutions are considered.

### MSC:

74A15 | Thermodynamics in solid mechanics |

74B99 | Elastic materials |

74H99 | Dynamical problems in solid mechanics |

35Q72 | Other PDE from mechanics (MSC2000) |

### Keywords:

Laplace transform; initial-boundary value problems; Green-Lindsay theory; piecewise-homogeneous media; Riesz-Fischer-Kupradze method
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\textit{T. Burchuladze}, Georgian Math. J. 1, No. 6, 587--598 (1994; Zbl 0806.73005)

### References:

[1] | V.D. Kupradze, T.G. Gegelia, M.O. Basheleishvili and T.V. Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. (Translated from Russian)North-Holland Publishing Company, Amsterdam-New-York-Oxford, 1979; Russian original;Nauka, Moscow, 1976. |

[2] | V.D. Kupradze and T.V. Burchuladze, Dynamical problems of the theory of elasticity and thermoelasticity. (Russian)Current Problems in Mathematics, v. 7 (Russian) 163–294,Itogi Nauki i Tekhniki Akad. Nauk SSSR, Vsesoyuzn. Inst. Nauchn. i Tekhnich. Inform., Moscow, 1975. · Zbl 0413.73002 |

[3] | T.V. Buchukuri, Some oscillation boundary value problems of elasticity theory with allowance for thermodiffusion. (Russian)Dokl. Akad. Nauk SSSR 235(1977), No. 2, 310–312. |

[4] | –, Boundary value problems of oscillation of moment thermodiffusion. (Russian)Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 7(1980), 5–56. |

[5] | T.V. Burchuladze, To the theory of dynamic problems of non-classical thermoelasticity. (Russian)Trudy Tbiliss. Mat. Inst. Razmadze 23 (1983), 12–24. · Zbl 0551.73013 |

[6] | –, Three-dimensional problems of non-classical thermoelasticity. (Russian)Trudy Tbiliss. Mat. Inst. Razmadze,25 (1984), 4–21. |

[7] | –, Dynamic problems of the non-classical theory of thermoelasticity. (Russian)Z. Anal. Anwendungen,3(1984), No. 5, 441–455. · Zbl 0565.73007 |

[8] | T.V. Burchuladze and T.G. Gegelia, The development of the method of potential in the elasticity theory. (Russian)Metsniereba, Tbilisi, 1985. · Zbl 0594.73026 |

[9] | T.V. Burchuladze, To the theory of dynamic problems of thermodiffusion of deformed elastic solid bodies. (Russian)Bull. Acad. Sci. Georgian SSR 89(1978), No. 2, 329–332. · Zbl 0377.73005 |

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