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On the theoretical justification of Pocklington's equation

Xavier Claeys 1 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : Pocklington's model consists in a one-dimensional integral equation relating the current at the surface of a straight finite wire to the tangential trace of an incident electromagnetic field. It is a simplification of the more usual single layer potential equation posed on a two-dimensional surface. We are interested in estimating the error between the solution of the exact integral equation and the solution of Pocklington's model. We address this problem for the model case of acoustics in a smooth geometry using results of asymptotic analysis.
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Submitted on : Wednesday, April 9, 2014 - 2:45:54 PM
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Xavier Claeys. On the theoretical justification of Pocklington's equation. Mathematical Models and Methods in Applied Sciences, 2009, 19 (8), pp.1325-1355. ⟨10.1142/S0218202509003802⟩. ⟨hal-00976012⟩



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