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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… Expand

Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces

- Zongben Xu, G. Roach
- Mathematics
- 1 May 1991

Abstract Let X be a real Banach space with dual X ∗ and moduli of convexity and smoothness δ X ( e ) and ϱ X ( τ ), respectively. For 1 p denotes the duality mapping from X into 2 X ∗ with gauge… Expand

Adomian's method for Hammerstein integral equations arising from chemical reactor theory

- N. M. Madbouly, D. McGhee, G. Roach
- Mathematics, Computer Science
- Appl. Math. Comput.
- 25 January 2001

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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… Expand

A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations

- Zongben Xu, G. Roach
- Mathematics
- 1 July 1992

Abstract A necessary and sufficient condition is established which ensures the strong convergence of the steepest descent approximation to a solution of equations involving quasi-accretive operators… Expand

The limiting-amplitude principle for the wave propagation problem with two unbounded media

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 reduced… Expand

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… Expand

An inverse transmission problem for the Helmholtz equation

- T. Angell, R. Kleinman, G. Roach
- Mathematics
- 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… Expand

On Mixed Boundary Value Problems of Dirichlet Oblique-Derivative Type in Plane Domains with Piecewise Differentiable Boundary

- J. Banasiak, G. Roach
- Mathematics
- 1 May 1989

In this paper we prove a decomposition formula of Grisvard type, but for mixed boundary value problems of Dirichlet-oblique derivative type for general elliptic equations of second order in a plane… Expand

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