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On the solvability of the three-dimensional first dynamic boundary value problem of hemitropic elasticity

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Abstract

We consider the first main dynamic boundary value problem for a three-dimensional piecewise homogeneous hemitropic micropolar medium. By using the Fourier method under sufficiently general assumptions, we prove the solvability of the problem in the classical sense.

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References

  1. Kupradze, V.D., Gegediya, T.G., Basheleishvili, M.O., and Burchuladze, T.V., Trekhmernye zadachi matematicheskoi teorii uprugosti i termouprugosti (Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity), Moscow: Nauka, 1976.

    Google Scholar 

  2. Kuvshinskii, E.V. and Aero, E.L., Continuum Theory of Asymmetric Elasticity. The Problem of “Internal” Rotation, Fiz. Tverd. Tela, 1963, vol. 5, no. 9, pp. 2591–2598.

    MathSciNet  Google Scholar 

  3. Nowacki, I.P. and Nowacki, W., Some Problems of Hemitropic Micropolar Continuum, Bull. Acad. Polon. Sci. Ser. Sci. Techn., 1977, vol. 25, pp. 1–14.

    Google Scholar 

  4. Kuvshinskii, E.V. and Aero, E.L., Continuum Theory of Asymmetric Elasticity. Equilibrium of Isotropic Body, Fiz. Tverd. Tela, 1964, vol. 6, no. 9, pp. 2689–2699.

    MathSciNet  Google Scholar 

  5. Bezhuashvili, Yu.A. and Rukhadze, R.V., On the Solution of the First Basic Three-Dimensional Problem for Hemitropic Micropolar Medium by the Fourier Method, Georgian Engineering News, 2010, vol. 2, no. 54, pp. 18–22.

    Google Scholar 

  6. Giorgashvili, L.G., Solution of Fundamental Boundary Value Problems of Statics for a Hemitropic Micropolar Medium, Tr. Tbiliss. Gos. Univ. Inst. Prikl. Mat., 1985, vol. 16, pp. 56–79.

    MathSciNet  MATH  Google Scholar 

  7. Natroshvili, D.G. and Dzhagmaidze, A.Ya., Dynamic Problems for Piecewise Homogeneous Bodies Taking into Account Moment Stresses, Tr. Tbiliss. Gos. Univ. Inst. Prikl. Mat., 1985, vol. 16, p. 25.

    MathSciNet  Google Scholar 

  8. Burchuladze, T. and Rukhadze, R., The Fourier Method in Three-Dimensional Boundary-Contact Dynamic Problems of Elasticity, Georgian Math. J., 1995, vol. 2, no. 6, pp. 555–576.

    Article  MathSciNet  Google Scholar 

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Original Russian Text © Yu.A. Bezhuashvili, R.V. Rukhadze, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 2, pp. 165–174.

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Bezhuashvili, Y.A., Rukhadze, R.V. On the solvability of the three-dimensional first dynamic boundary value problem of hemitropic elasticity. Diff Equat 49, 166–175 (2013). https://doi.org/10.1134/S0012266113020031

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