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Asymptotic solutions of the elastic wave equation and reflected waves near boundaries

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In the first half of this paper, we construct asymptotic solutions of linear anisotropic elastic equations. In the latter half, we investigate waves reflected by boundaries for plane incident waves in terms of these solutions. Especially, it is examined whether or not the mode-conversion occurs near points where the incident waves hit the boundaries perpendicularly.

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References

  1. Friedrichs, K. O.: Symmetric hyperbolic system of linear differential equations. Commun. Pure Appl. Math.7, 345–392 (1954)

    Google Scholar 

  2. Karal, F. C., Keller, J. B.: Elastic wave propagation in homogeneous and inhomogeneous media. J. Acaustic. Soc. Am.31, 694–705 (1959)

    Google Scholar 

  3. Lax, P.: Asymptotic solutions of oscillatory initial value problems. Duke Math. J.24, 627–646 (1957)

    Google Scholar 

  4. Mizohata, S.: The theory of partial differential equations. Cambridge University Press: London 1973

    Google Scholar 

  5. Soga, H.: Asymptotic solutions of the elastic wave equation and their applications. Bull. Fac. Educ., Ibaraki Univ. (Nat. Sci.)38, 9–16 (1989)

    Google Scholar 

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Communicated by H. Araki

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Soga, H. Asymptotic solutions of the elastic wave equation and reflected waves near boundaries. Commun.Math. Phys. 133, 37–52 (1990). https://doi.org/10.1007/BF02096553

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  • DOI: https://doi.org/10.1007/BF02096553

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