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In this paper we determine exact, analytical solutions of the parabolic, nonlinear diffusion equation θ t = ( f 2 (θ)θ x ) x + f 1 (θ), in which we insist that at least one of f 1 and f 2 is arbitrary. To do this we find reductions of the equation using a method based on the Clarkson and...
We investigate the initial-boundary value problem for Maxwell's equations in linear conducting materials together with dissipative boundary conditions. We show that it is possible to introduce the free energy and derive from it a domain of dependence. We prove the existence, uniqueness and...
Time-harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle embedded in a chiral environment. The corresponding transmission problem is reduced, via Bohren's decomposition, to an integral equation over the interface between the obstacle and the surrounding medium. This...
The Neumann problem for the propagative Helmholtz equation in the exterior of several bodies (obstacles) is studied in two and three dimensions by a special modification of the boundary integral equation method. This modification can be called the 'method of interior boundaries', because...
In this paper a proof of existence and non-existence of the conically self-similar free-vortex solutions to the Navier-Stokes equations, originally found by Yih et al. (1982, Phys. Fluids. 25, 2147-2158), is presented. This proof clearly establishes that these solutions do not have any kind of...
The vibration of an infinite membrane supported by a square or triangular array of circular posts is studied by eigenfunction expansion and collocation. The fundamental frequencies are found to be highly sensitive to both small and large relative post radii b . The singular nature of the...
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