Related papers: Enhancement of combustion by drift in a coupled re…
We study flow-induced enhancement of the speed of pulsating traveling fronts for reaction-diffusion equations, and quenching of reaction by fluid flows. We prove, for periodic flows in two dimensions and any combustion-type reaction, that…
This paper is devoted to the study of the asymptotic behaviors of the minimal speed of propagation of pulsating traveling fronts solving the Fisher-KPP reaction-advection-diffusion equation within either a large drift, a mixture of large…
We obtain a criterion for pulsating front speed-up by general periodic incompressible flows in two dimensions and in the presence of KPP nonlinearities. We achieve this by showing that the ratio of the minimal front speed and the effective…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…
We consider reaction-diffusion equations with combustion-type non-linearities in two dimensions and study speed-up of their pulsating fronts by general periodic incompressible flows with a cellular structure. We show that the occurence of…
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of…
This Note is concerned with the asymptotic behavior of the minimal KPP speed of propagation for reaction- advection-diffusion equations with a large drift Mq (where q is the advection). We first give the limit of the speed as…
We study the velocity of travelling waves of a reaction-diffusion system coupling a standard reaction-diffusion equation in a strip with a one-dimensional diffusion equation on a line. We show that it grows like the square root of the…
We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main…
We take interest in a reaction-diffusion system which has been recently proposed [11] as a model for the effect of a road on propagation phenomena arising in epidemiology and ecology. This system consists in coupling a classical Fisher-KPP…
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…
We consider in this paper a reaction-diffusion system under a KPP hypothesis in a cylindrical domain in the presence of a shear flow. Such systems arise in predator-prey models as well as in combustion models with heat losses. Similarly to…
We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coefficient is a fixed bounded monotone profile that is shifted at…
In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…
We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the…
We consider one-dimensional reaction-diffusion equations of Fisher-KPP type with random stationary ergodic coefficients. A classical result of Freidlin and Gartner [16] yields that the solutions of the initial value problems associated with…
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…