A modification of the parabolic Allen–Cahn equation, determined by the substitution of Fick’s diffusion law with a relaxation relation of Cattaneo-Maxwell type, is considered. The analysis concentrates on traveling fronts connecting the two stable states of the model, investigating both the aspects of existence and stability. The main contribution is the proof of the nonlinear stability of the ...

This paper describes a very general absorbing layer model for hyperbolic-parabolic systems of partial differential equations. For linear systems with constant coefficients it is shown that the model possesses the perfect matching property, i.e., it is a perfectly matched layer (PML). The model is applied to two linear systems: a linear wave equation with a viscous damping term and the linearize...

Abstract. We develop an algorithm for the canonical computation of general Fourier integral operators whose canonical relations are graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation of the action of such operators on data in the presence of caustics. The procedure consists in the construction of a universal operat...

A semi-empirical model for surf zone wave height decay is adapted to the parabolic equation method in order to include the effect of depth-limited wave breaking in combined refraction/diffraction calculations. Several examples for plane beaches are presented in order to show correspondence between the empirical model, its numerical formulation, and previous laboratory data. The model is then ap...

We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation of the action of such operators on data in the presence of caustics. The procedure consists in the construction of a universal operator representation throug...

In this paper we investigate the asymptotic spatial behavior of the solutions for several models for the nerve fibers. First, our analysis deals with the coupling of two parabolic equations. We prove that, under suitable assumptions on the coefficients and the nonlinear function, the decay is similar to the one corresponding to the heat equation. A limit case of this system corresponds to the c...

Observations of seismic waves from earthquakes at depths between 100 and 200 km beneath Japan show that the initial portion of the S-wave arrival has greater duration than can be accounted for by earthquake source-time duration. The observed long duration of S waves has been explained as being caused by multiple forward scattering around the ray path between source and receiver. Array observati...

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