Related papers: Generalized transition waves and their properties
We consider a wave equation with a time-dependent propagation speed, whose potential oscillations are controlled through bounds on its first and second derivatives and by limiting the integral of the difference with a fixed constant. We…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
We define ultradistributional wave front sets with respect to translation-modulation invariant Banach spaces of ultradistributions having solid Fourier image. The main result is their characterisation by the short-time Fourier transform.
In this paper, we study univariate and planar random motions with variable propagation speeds. We first consider motions with space-varying velocity, which can be reduced to constant-velocity motions by means of suitable nonlinear…
Propagation of transition fronts in models of coupled oscillators with non-degenerate on-site potential is usually considered in terms of travelling waves. We show that the system dynamics can be reformulated as an implicit map structure,…
In this paper, we give characterizations of usual wave front set and Sobolev type wave front set in terms of wave packet transform without any restriction on basic wave packet.
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
We investigate necessary and sufficient conditions for the extendibility and boundedness of Gaussian curvature, Mean curvature and principal curvatures near all types of singularities on fronts. We also study the convergence to infinite…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
We consider the propagation of a flame front in a solid medium with a periodic structure. The model is governed by a free boundary system for the pair" temperature-front. "The front's normal velocity depends on the temperature via a…
This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by…
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this…
In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…
We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…
One can define several properties of wave equations that correspond to the absence of tails in their solutions, the most common one by far being Huygens' principle. Not all of these definitions are equivalent, although they are sometimes…