In this paper we study the application of boundary integral equation methods to the solution of the Helmholtz equation in a locally perturbed half–plane with Robin or impedance boundary conditions. This problem models outdoor noise propagation from a cutting onto a surrounding flat plane, and also the harbour resonance problem in coastal engineering. We… (More)
We study the codimension-one and-two bifurcations of the Ornstein–Zernike equation with hypernetted chain (HNC) closure with Lennard–Jones intermolecular interaction potential. The main purpose of the paper is to present the results of a numerical study undertaken using a suite of algorithms implemented in MATLAB and based on pseudo arc-length continuation… (More)
We consider a class of degenerate diffusion equations where the nonlinearity is assumed to be singular (non-Lipschitz) at zero. It is shown that solutions with compactly supported initial data become identically zero in finite time. Such extinction follows by comparison with newly constructed finite travelling waves connecting two stable equilibria.