Solvability of singular integral system connected with seismic waves around the borehole |
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Authors: | Leïla Alem Lahcne Chorfi |
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Institution: | Leïla Alem,Lahcène Chorfi |
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Abstract: | We study in this article a boundary‐value problem arising in the propagation of waves in an elastic half‐space covered by a layer with a vertical borehole. We first show a uniqueness theorem under some restrictions on the solution. For the existence, we use the direct integral equation method. We obtain a singular integral system on the half‐line. For the solvability, we reduce this system to an elliptic pseudodifferential equation and establish the Fredholm property. Finally, we compute the index of the associated operator for various values of Poisson's ratio. Copyright © 2006 John Wiley & Sons, Ltd. |
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Keywords: | elastic waves singular integral equations fredholm property |
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