相关论文: An exactly soluble noisy traveling wave equation a…
In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
Using the relation of a set of nonlinear Langevin equations with reaction-diffusion processes, we note the existence of a maximal strength of the noise for the stochastic traveling wave solutions of these equations. Its determination is…
In this note, we investigate a doubly nonlinear diffusion equation in the slow diffusion regime. We prove stability of the pressure of solutions that are close to traveling wave solutions in a homogeneous Lipschitz sense. We derive…
In this study, we analyze the behavior of monotone traveling waves of a one-dimensional porous medium equation modeling mechanical properties of living tissues. We are interested in the asymptotics where the pressure, which governs the…
In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a…
We analyze the dynamics of particles in two dimensions with constant speed and a stochastic switching angle dynamics defined by a correlated dichotomous Markov process (telegraph noise) plus Gaussian white noise. We study various cases of…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…
We present in this paper the construction of a continuum directed polymer model in an environment given by space-time L\'evy noise. One of the main objectives of this construction is to describe the scaling limit of discrete directed…
We consider in this paper travelling wave solutions to stochastic partial differential equations and corresponding wave speed. As a particular example we consider the Nagumo equation with multiplicative noise which we mainly consider in the…
We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
The one-dimensional motion of any number $\cN$ of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We consider a stochastic model of N evolving particles studied by Brunet and Derrida. This model can be seen as a directed polymer in random medium with N sites in the transverse direction. Cook and Derrida, use heuristic arguments to…
We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
In this paper we investigate stability of travelling wave solutions to a class of reaction-diffusion equations perturbed by infinite-dimensional additive noise with H\"older continuous paths, covering in particular fractional Brownian…