caa a22 4500 386383154 CHVBK 20180307112049.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500018564 doi S0308210500018564 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500018564 The approximation of exterior Neumann problems in a halfspace by means of problems with compact boundary [Elektronische Daten] This paper describes a proof that the solutions of Neumann problems for the exterior of spheres {x ∊ ℝ3∣ converge to the solutions of the exterior problem for the halfspace {x ∊ ℝ3 } x1 ≧ 0} as b → ∞ provided that the boundary data converge in a certain sense. The method requires that there be some dissipation which can be arbitrarily small. Fredholm integral equations are set up for the boundary data, and these are solved by means of Neumann series for large b. Estimates on the terms of the series (which involve singular integrals), in terms of b, allow the convergence proof to be carried through. The procedure of expressing problems with infinite boundaries in terms of problems with finite boundaries allows the implementation of an effective numerical procedure for determining, for example, the entire near-field of a baffled piston, a problem whose solution has proved elusive for many years. Copyright © Royal Society of Edinburgh 1989 Becker Ronald I. Department of Mathematics, University of Cape Town, Rondebosch 7700, South Africa New Ronald Central Acoustics Laboratory, University of Cape Town, Rondebosch 7700, South Africa Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/3-4(1989), 285-300 0308-2105 111:3-4<285 1989 111 PRM https://doi.org/10.1017/S0308210500018564 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500018564 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Becker Ronald I. Department of Mathematics, University of Cape Town, Rondebosch 7700, South Africa NATIONALLICENCE 700 1- New Ronald Central Acoustics Laboratory, University of Cape Town, Rondebosch 7700, South Africa NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/3-4(1989), 285-300 0308-2105 111:3-4<285 1989 111 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge