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Decaying and nondecaying properties of the local energy of an elastic wave outside an obstacle

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Abstract

We consider the decaying mode of the local energy of the solution of an initial boundary value problem in the exterior region outside a spherical obstacle for the equation of elasticity as time tends to infinity. It is shown that Rayleigh’s surface wave prevents the exponential decay of the local energy in the case of the Neumann boundary condition and that the local energy blows up at the rate of the square of the time variable in the case of the Robin boundary condition.

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Author notes

  1. Masaru Ikehata

    Present address: Dept. Appl. Phys., Fac. Engrg., Nagoya Univ., 464, Nagoya, Japan

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Tokyo Metropolitan University, Fukasawa, Setagaya-ku, 158, Tokyo, Japan

    Masaru Ikehata

  2. Department of Mathematics, Faculty of Science, Josai University, 350, Sakado, Saitama, Japan

    Gen Nakamura

Authors
  1. Masaru Ikehata
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  2. Gen Nakamura
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Ikehata, M., Nakamura, G. Decaying and nondecaying properties of the local energy of an elastic wave outside an obstacle. Japan J. Appl. Math. 6, 83–95 (1989). https://doi.org/10.1007/BF03167917

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  • DOI: https://doi.org/10.1007/BF03167917

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