Related papers: Proliferating L\'evy Walkers and Front Propagation
In this paper we use the theory of viscosity solutions for Hamilton-Jacobi equations to study propagation phenomena in kinetic equations. We perform the hydrodynamic limit of some kinetic models thanks to an adapted WKB ansatz. Our models…
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…
This paper is concerned with the spreading speeds of nonlocal dispersal predator-prey systems in shifting habitats under general initial conditions. By employing geometric optics techniques and theory of viscosity solutions, we reformulate…
We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on…
Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times…
This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
The purpose of this paper is to implement a random death process into a persistent random walk model which produces subballistic superdiffusion (L\'{e}vy walk). We develop a Markovian model of cell motility with the extra residence variable…
Nonlinear and nonlinear evolution equations of the form $u_t=\L u \pm|\nabla u|^q$, where $\L$ is a pseudodifferential operator representing the infinitesimal generator of a L\'evy stochastic process, have been derived as models for growing…
We study the dispersion of a particle whose motion dynamics can be described by a forced velocity jump process. To investigate large deviations results, we study the Chapman-Kolmogorov equation of this process in the hyperbolic scaling…
Subdiffusive motion takes place at a much slower timescale than diffusive motion. As a preliminary step to studying reaction-subdiffusion pulled fronts, we consider here the hyperbolic limit $(t,x) \to (t/\varepsilon, x/\varepsilon)$ of an…
We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range of…
Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predator-prey model of reaction-diffusion type to analyze the…
We investigate the dynamic impact of heterogeneous environments on superdiffusive random walks known as L\'evy flights. We devote particular attention to the relative weight of source and target locations on the rates for spatial…
The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is…
We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B $\to$ 2A reaction. We…
L\'{e}vy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…
Standard Reaction-Diffusion (RD) systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle…