Enhancement of combustion by drift in a coupled reaction-diffusion model

Fast drift effects in the averaging of a filtration combustion system - a periodic homogenization approach

We target at the periodic homogenization of a semi-linear reaction-diffusion-convection system describing filtration combustion, where fast drifts affect the competition between heat and mass transfer processes as well as the interplay between the surface nonlinear chemical reactions and the transport processes. To handle the heterogeneity of the medium, we rely on the concept of two-scale convergence with drift to obtain for suitably scaled model parameters the upscaled system of combustion equations together with the effective transport and reaction parameters. The main difficulty here is to…

Reaction-Diffusion Front Speed Enhancement by Flows

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 the front speed is proportional to the square root of the (homogenized) effective diffusivity of the flow. We show that this result does not hold in three and more dimensions. We also prove conjectures from [1,3,11] for cellular flows, concerning the rate of speed-up of fronts and the minimal flow amplitude necessary to quench solutions with initial data of a…

关于平均量的弛豫时间的大漂移增强

On Large Drift Enhancement for the Relaxation Time of Averages

本注记在类似相关研究的分析框架下，利用Chatterjee 2025年的奇异值间隙方法，证明了存在大不可压缩漂移类项时平均量的L²弛豫时间渐近消失的一般性结果。