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Some theorems in classical elastodynamics

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References

  1. Kellogg, O.D., Foundations of Potential Theory. New York: Dover 1953.

    Google Scholar 

  2. Mikusinski, J., Operational Calculus. New York: Pergamon Press 1959.

    Google Scholar 

  3. Neumann, F., Vorlesungen über die Theorie der Elasticität der festen Körper und des Lichtäthers. Leipzig: B. G. Teubner 1885.

    Google Scholar 

  4. Graffi, D., Sul teorema di reciprocitá nella dinamica dei corpi elastici. Memorie della Accademia delle Scienze, Bologna, Series 10, 4, 103 (1946/47).

    Google Scholar 

  5. Zaremba, S., Sopra un teorema d'unicitá relativo alla equazione delle onde sferiche. Atti della Reale Accademia dei Lincei, Series 5, 24, 904 (1915).

    Google Scholar 

  6. Bers, L., F. John, & M. Schechter, Partial Differential Equations. New York: Interscience Publishers 1964.

    Google Scholar 

  7. Rubinowicz, A., Herstellung von Lösungen gemischter Randwertprobleme bei hyperbolischen Differentialgleichungen zweiter Ordnung durch Zusammenstückelung aus Lösungen einfacher gemischter Randwertaufgaben. Monatshefte für Mathematik und Physik, 30, 65 (1920).

    Google Scholar 

  8. Friedrichs, K.O., & H. Lewy, Über die Eindeutigkeit und das Abhängigkeitsgebiet der Lösungen beim Anfangswertproblem linearer hyperbolischer Differentialgleichungen. Mathematische Annalen, 98, 192 (1928).

    Google Scholar 

  9. Courant, R., Partial Differential Equations, Volume 2 of Methods of Mathematical Physics by R. Courant, & D. Hilbert. New York: Interscience Publishers 1962.

    Google Scholar 

  10. Gurtin, M.E., & E. Sternberg, A note on uniqueness in classical elastodynamics. Quarterly Applied Mathematics, 19, 169 (1961).

    Google Scholar 

  11. Gurtin, M.E., & R. A. Toupin, A uniqueness theorem for the displacement boundary-value problem of linear elastodynamics. Quarterly of Applied Mathematics, 23, 79 (1965).

    Google Scholar 

  12. Knops, R.J., & L.E. Payne, Uniqueness in classical elastodynamics. Archive for Rational Mechanics and Analysis, 27, 349 (1968).

    Google Scholar 

  13. Fichera, G., Sull'esistenza e sul calcolo delle soluzioni dei problemi al contorno, relativi all'equilibrio di un corpo elastico. Annali della Scuola Normale Superiori di Pisa, Ser.III, 4, 35 (1950).

    Google Scholar 

  14. Gurtin, M.E., & E. Sternberg, Theorems in elastostatics for exterior domains. Archive for Rational Mechanics and Analysis, 8, 99 (1961).

    Google Scholar 

  15. Turteltaub, M.J., & E. Sternberg, Elastostatic uniqueness in the half-space. Archive for Rational Mechanics and Analysis, 24, 233 (1967).

    Google Scholar 

  16. Dieudonné, J., Foundations of Modern Analysis. New York: Academic Press 1960.

    Google Scholar 

  17. Stokes, G.G., On the dynamical theory of diffraction. Transactions of the Cambridge Philosophical Society, 9, 1 (1849).

    Google Scholar 

  18. Love, A.E.H., The propagation of wave-motion in an isotropic elastic solid medium. Proceedings of the London Mathematical Society, Series 2, 1, 291 (1904).

    Google Scholar 

  19. Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity. Fourth edition, New York: Dover1944.

    Google Scholar 

  20. Thomson, W. (Lord Kelvin), & P. G. Tait, Treatise on Natural Philosophy (reprinted as Principles of Mechanics and Dynamics), Part II. New York: Dover 1962.

    Google Scholar 

  21. Sternberg, E., & R. A. Eubanks, On the concept of concentrated loads and an extension of the uniqueness theorem in the linear theory of elasticity. Journal of Rational Mechanics and Analysis, 4, 135 (1955).

    Google Scholar 

  22. Kirchhoff, G., Zur Theorie der Lichtstrahlen. Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, Berlin, Zweiter Halbband, 641 (1882).

    Google Scholar 

  23. Somigliana, C., Sulle equazioni della elasticitá. Annali di Matematica, Series 2, 17, 37 (1889).

    Google Scholar 

  24. Volterra, V., Sur les vibrations des corps élastiques isotropes. Acta Mathematica, 18, 161 (1894).

    Google Scholar 

  25. de Hoop, A.T., Representation theorems for the displacement in an elastic solid and their application to elastodynamic diffraction theory. Doctoral Dissertation, Technische Hogeschool, Delft (1958).

    Google Scholar 

  26. Somigliana, C., Sopra alcune formole fondamentali della dinamica dei mezzi isotropi. Atti della Reale Accademia delle Scienze di Torino, 41, 869 (1905/6); 41, 1071 (1905/6); 42, 387 (1906/7).

    Google Scholar 

  27. Tedone, O., Sulle vibrazioni dei corpi solidi, omogenei ed isotropi. Memorie della Reale Accademia delle Scienze di Torino 47, 181 (1896/97).

    Google Scholar 

  28. Turteltaub, M.J., & E. Sternberg, On concentrated loads and Green's functions in elastostatics. Archive for Rational Mechanics and Analysis 29, 193 (1968).

    Google Scholar 

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Wheeler, L.T., Sternberg, E. Some theorems in classical elastodynamics. Arch. Rational Mech. Anal. 31, 51–90 (1968). https://doi.org/10.1007/BF00251514

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