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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Authors: | Antonios Charalambopoulos |
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Institution: | (1) Department of Mathematics, National Technical University of Athens, Athens, Greece |
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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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