## Journal of Integral Equations and Applications

### An Integral Equation Method for a Boundary Value Problem Arising in Unsteady Water Wave Problems

#### Article information

Source
J. Integral Equations Applications, Volume 20, Number 1 (2008), 121-152.

Dates
First available in Project Euclid: 25 March 2008

https://projecteuclid.org/euclid.jiea/1206475809

Digital Object Identifier
doi:10.1216/JIE-2008-20-1-121

Mathematical Reviews number (MathSciNet)
MR2396957

Zentralblatt MATH identifier
1134.76007

#### Citation

Preston, M.D.; Chamberlain, P.G.; Chandler-Wilde, S.N. An Integral Equation Method for a Boundary Value Problem Arising in Unsteady Water Wave Problems. J. Integral Equations Applications 20 (2008), no. 1, 121--152. doi:10.1216/JIE-2008-20-1-121. https://projecteuclid.org/euclid.jiea/1206475809

#### References

• T. Arens, S.N. Chandler-Wilde and K. Haseloh, Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions, J. Math. Anal. Appl. 272, (2002), 276-302.
• --------, Solvability and spectral properties of integral equations on the real line: II. $L^p$ spaces and applications, J. Int. Equations Appl. 15 (2003), 1-35.
• J.T. Beale, A convergent boundary integral equation method for three-dimensional water waves, Math. Comp. 70 (2001), 977-1029.
• J.T. Beale, T.Y. Hou and J. Lowengrub, Convergence of a boundary integral method for water waves, SIAM J. Numer. Anal. 33 (1996), 1797-1843.
• S.N. Chandler-Wilde, E. Heinemeyer and R. Potthast, Acoustic scattering by mildly rough unbounded surfaces in three dimensions, SIAM J. Appl. Math. 66 (2006), 1002-1026.
• S.N. Chandler-Wilde and C.R. Ross, Scattering by rough surfaces: The Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane, Math. Meth. Appl. Sci. 19 (1996), 959-976.
• D. Colton and R. Kress, Integral equation methods in scattering theory, Wiley, New York, 198-3.
• C. Fochesato and F. Dias, A fast method for nonlinear three-dimensional free-surface waves, Proc. Royal Soc. London 462 (2006), 2715-2735.
• L. Fraenkel, Introduction to maximum principles and symmetry in elliptic problems, CUP, 200-0.
• D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer, New York, 197-7.
• N.M. Günter, Potential theory and its applications to basic problems of mathematical physics, Ungar, New York, 196-8.
• J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, New Haven, CT, 192-3.
• T.Y. Hou and P. Zhang, Convergence of a boundary integral method for 3-d water waves, Discrete Contin. Dyn. Sys. 2 (2002), 1-34.
• R. Kress, Linear integral equations, Springer, New York, 199-9.
• Y. Meyer and R. Coifman, Wavelets: Calderon-Zygmund and multilinear operators, CUP, 200-0.
• S. Mikhlin, An advanced course of mathematical physics, North-Holland, Amsterdam, 197-0.
• A.T. Peplow and S.N. Chandler-Wilde, Approximate solution of second kind integral equations on infinite cylindrical surfaces, SIAM J. Numer. Anal. 32 (1995), 594-609.
• M.D. Preston, A boundary integral equation method for a boundary value problem arising in unsteady water waves, Ph.D. thesis, University of Reading, Reading, UK, 200-7.
• G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains, J. Funct. Anal. 59 (1984), 572-611.