Transmission problems for the Helmholtz equation
A straightforward treatment of these problems is given which appears to avoid many of the previously encountered difficulties. Admittedly some generality is lost by assuming that the various…
Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
- Zongben Xu, G. Roach
- Mathematics
- 1 May 1991
Adomian's method for Hammerstein integral equations arising from chemical reactor theory
- N. M. Madbouly, D. McGhee, G. Roach
- MathematicsApplied Mathematics and Computation
- 25 January 2001
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
- G. Roach, I. Stratis, A. Yannacopoulos
- Mathematics
- 4 March 2012
A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations
- Zongben Xu, G. Roach
- Mathematics
- 1 July 1992
Boundary Integral Equations for the Three-Dimensional Helmholtz Equation
- R. Kleinman, G. Roach
- Mathematics
- 1 April 1974
The relation between various boundary integral equation formulations of Dirichlet and Neumann problems for the three-dimensional Helmholtz equation is clarified. The integral equations derived using…
Weak Solutions of Fluid–Solid Interaction Problems
- G. Hsiao, R. Kleinman, G. Roach
- Mathematics
- 1 October 2000
This paper is concerned with various variational formulations for the fluid–solid interaction problems. The basic approach here is a coupling of field and boundary integral equation methods. In…
The limiting-amplitude principle for the wave propagation problem with two unbounded media
Abstract In this paper, we consider the diffraction problem for wave propagation in inhomogeneous, penetrable media with an unbounded interface. The low frequency behaviour of the resolvent for the…
On Sommerfeld radiation conditions for the diffraction problem with two unbounded media
Synopsis A radiation condition is obtained, and is then used together with weighted Sobolev spaces and the limiting absorption method to establish the unique existence of solutions to the diffraction…
An inverse transmission problem for the Helmholtz equation
- T. Angell, R. Kleinman, G. Roach
- Mathematics, Business
- 1 May 1987
The problem considered is that of determining the shape of a three-dimensional scattering object, illuminated by an acoustic field, from a knowledge of scattered far-field data. The far-field data…
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