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An integral equation method for a boundary value problem arising in unsteady water wave problems

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Preston, M. D., Chamberlain, P. G. and Chandler-Wilde, S. N. (2008) An integral equation method for a boundary value problem arising in unsteady water wave problems. Journal of Integral Equations and Applications, 20 (1). pp. 121-152. ISSN 0897-3962

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To link to this article DOI: 10.1216/JIE-2008-20-1-121

Abstract/Summary

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:1161
Publisher:Rocky Mountain Mathematics Consortium

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