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Morawetz's method for the decay of the solution of the exterior initial-boundary value problem for the linearized equation of dynamic elasticity

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Abstract

In this paper, the behavior of the solution of the time-dependent linearized equation of dynamic elasticity is examined.

For the homogeneous problem, it is proved that in the exterior of a star-shaped body on the surface of which the displacement field is zero, the solution decays at the rate t -1 as the time t tends to infinity.

For the non-homogeneous problem with a harmonic forcing term, it is proved that for large times, the elastic material in the exterior of the body, tends to a harmonic motion, with the period of the external force.

The convergence to the steady harmonic state solution is at the rate t -1/2 as t tends to infinity, and is uniform on bounded sets.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Antonios Charalambopoulos

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  1. Antonios Charalambopoulos
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Charalambopoulos, A. Morawetz's method for the decay of the solution of the exterior initial-boundary value problem for the linearized equation of dynamic elasticity. J Elasticity 31, 47–69 (1993). https://doi.org/10.1007/BF00041623

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  • DOI: https://doi.org/10.1007/BF00041623

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