相关论文: Traveling waves in reaction-diffusion system
In this paper, we extend and complement previous works about propagation in kinetic reaction-transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction…
We consider a scalar parabolic equation in one spatial dimension. The equation is constituted by a convective term, a reaction term with one or two equilibria, and a positive diffusivity which can however vanish. We prove the existence and…
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…
We consider the motion of planar phase-transition fronts in first-order phase transitions of the Universe. We find the steady state wall velocity as a function of a friction coefficient and thermodynamical parameters, taking into account…
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a standard local stability analysis, numerical bifurcation…
An approximate analytical approach to describe the stochastic motion of sound rays in deep ocean is developed. This is done for a realistic propagation model with an internal wave induced perturbation imposed on the smooth background sound…
We study a singular diffusive prey-predator system with nonlocal dispersal for which the carrying capacity of the predator is proportional to the density of prey. We show the existence of positive one-dimensional traveling waves connecting…
We study front propagation in the reaction diffusion process $\{A\stackrel{\epsilon}\to2A, A\stackrel {\epsilon_t}\to3A\}$ on a one dimensional (1d) lattice with hard core interaction between the particles. Using the leading particle…
We consider the moving particle process in Rd which is defined in the following way. There are two independent sequences (Tk) and (dk) of random variables. The variables Tk are non negative and form an increasing sequence, while variables…
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…
Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
We jointly investigate the existence of quasi-stationary distributions for one dimensional L\'evy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion.…
We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum of the linearised operator in full generality and identify…
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 establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
We investigate the connection between the existence of an explicit travelling wave solution and the travelling wave with minimal speed in a scalar monostable reaction-diffusion equation.
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
We investigate the effect of a Heaviside cut-off on the front propagation dynamics of the so-called Burgers-FisherKolmogoroff-Petrowskii-Piscounov (Burgers-FKPP) advection-reaction-diffusion equation. We prove the existence and uniqueness…
This paper deals with the existence of traveling fronts guided by the medium for a KPP reaction-diffusion equation coming from a model in population dynamics in which there is spatial spreading as well as genetic mutation of a quantitative…