Efficient parallel-in-time methods for hyperbolic partial differential equation problems remain scarce. Here we investigate an approach based on circulant preconditioned generalised minimal residual (GMRES) the monolithic block Toeplitz equations which arise from constant time-step discretizations. We present theoretical results guarantee convergence in a number of iterations independent time-s...

Wave propagation in curved tubular domains is considered. A general version of Webster’s equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of the wave equation satisfy the corresponding Webster’s equation when the latter includes additional control signals determined by the solution.

In this paper, we prove the local well-posedness of the water wave problem with surface tension in the case of finite depth by working in the Eulerian setting. For the flat bottom, as surface tension tends to zero, the solution of the water wave problem with surface tension converges to the solution of the water wave problem without surface tension.

Evanescent wave spectroscopy using thin optically transparent electrodes and multiple reflections allows unique observations of the electrochemical interphase since the region of solution sampled is typically 100 nm from the electrode in the visible spectral region. This technique is found to be highly sensitive to the presence of absorbing adsorbed species

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...