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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 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.
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)