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On the stability of integral equations of the first kind with logarithmic kernels

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Abstract

This paper discusses the stability of the Galerkin method for a class of boundary integral equations of the first kind. These integral equations arise in acoustics, elasticity, and hydrodynamics, and the kernels of the principal parts of the corresponding integral operators all have logarithmic singularities. It is shown that an optimal choice of the mesh size can be made in the numerical computation so that one will obtain an optimal rate of convergence of the approximate solutions. The results here are consistent with those obtained by the Tikhonov regularization procedure.

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  1. Department of Mathematical Sciences, University of Delaware, Newark

    George C. Hsiao

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  1. George C. Hsiao
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Communicated by G. Fichera

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Hsiao, G.C. On the stability of integral equations of the first kind with logarithmic kernels. Arch. Rational Mech. Anal. 94, 179–192 (1986). https://doi.org/10.1007/BF00280433

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  • DOI: https://doi.org/10.1007/BF00280433

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