Related papers: Propagation for KPP bulk-surface systems in a gene…
This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. These similarities make it possible to prove, among other results, an extinction…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear…
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky- Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to…
We recently formulated the canonical boundary-value problem of propagation of surface plasmon-polariton (SPP) waves along the direction of periodicity of a one-dimensional photonic crystal. Here we present the general formulation of that…
We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of…
We study propagation over $\mathbb{R}^d$ of the solution to a nonlocal nonlinear equation with anisotropic kernels, which can be interpretted as a doubly nonlocal reaction-diffusion equation of the Fisher--KPP-type. We prove that if the…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
We theoretically demonstrate coherent control over propagation of surface plasmon polaritons(SPP), at both telecommunication and visible wavelengths, on a metallic surface adjacent to quantum coherence (phaseonium) medium composed of…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
The minimal speeds ($c^*$) of the Kolmogorov-Petrovsky-Piskunov (KPP) fronts at small diffusion ($\epsilon \ll 1$) in a class of time-periodic cellular flows with chaotic streamlines is investigated in this paper. The variational principle…
The Fisher-KPP equation is a reaction-diffusion equation originally proposed by Fisher to represent allele propagation in genetic hosts or population. It was also proposed by Kolmogorov for more general applications. A novel method for…
The goal of this paper is to find the homogenized equation of a heterogenous Fisher-KPP model in a periodic medium. The solutions of this model are pulsating travelling fronts whose \emph{speeds} are superior to a parametric minimal speed…
In this paper, we investigate stochastic heat equation with sublinear diffusion coefficients. By assuming certain concavity of the diffusion coefficient, we establish non-trivial moment upper bounds and almost sure spatial asymptotic…
We investigate the influence of fluid flows on the propagation of chemical fronts arising in FKPP type models. We develop an asymptotic theory for the front speed in a cellular flow in the limit of small molecular diffusivity and fast…
This paper is concerned with the existence and further properties of propagation speeds of transition fronts for bistable reaction-diffusion equations in exterior domains and in some domains with multiple cylindrical branches. In exterior…
We propose a scheme to study the nonlinear propagation properties of nonlinear surface plasmon polaritons (SPPs) in a three level $\Lambda$ type electromagnetically induced transparency (EIT) system with modulation of a rectangular barrier.…
We consider the spreading dynamics of the Fisher-KPP equation in a shifting environment, by analyzing the limit of the rate function of the solutions. For environments with a weak monotone condition, it was demonstrated in a previous paper…
The propagation of nonlinear and dispersive waves in various materials can be described by the well-known Kadomtsev-Petviashvili (KP) equation, which is a (2+1)-dimensional partial differential equation. In this paper, we show that the KP…