Related papers: Traveling waves in a mean field learning model
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…
The notion of traveling wave, which typically refers to some particular spatio-temporal con- nections between two stationary states (typically, entire solutions keeping the same profile's shape through time), is essential in the…
In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion,…
A unified geometric approach for the stability analysis of traveling pulse solutions for reaction-diffusion equations with skew-gradient structure has been established in a previous paper [9], but essentially no results have been found in…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
Recently a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other non-linear theories the new approach has the advantage that it provides a full time-dependent description of the…
We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…
We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed $\epsilon^{-1}$ ($\epsilon\textgreater{}0$), and proliferate according to a reaction…
Spreading processes play an increasingly important role in modeling for diffusion networks, information propagation, marketing and opinion setting. We address the problem of learning of a spreading model such that the predictions generated…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…
This paper is concerned with traveling waves to an diffusive SIR model with delay placed in the diffusion terms as well as nonlinear incidence rate with delay. Using a cross iteration scheme and partial monotone conditions it will be shown…
In this article, we are interested in a non-monotone system of logistic reaction-diffusion equations. This system of equations models an epidemics where two types of pathogens are competing, and a mutation can change one type into the other…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
For scalar reaction-diffusion equations, a traveling wave is a front which transforms a higher energy state to a lower energy state. The same is true for a system of equations with a gradient structure. At the core of this phenomenon, the…
We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less…
This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial…
Traveling waves of neural activity are widely observed in the brain, but their precise computational function remains unclear. One prominent hypothesis is that they enable the transfer and integration of spatial information across neural…
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field…
In this paper we consider a scalar parabolic equation on a star graph; the model is quite general but what we have in mind is the description of traffic flows at a crossroad. In particular, we do not necessarily require the continuity of…