Related papers: Studying wildfire fronts using advection-diffusion…
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents…
Given the recent increase in wildfires, developing a better understanding of their dynamics is crucial. For this purpose, the advection-diffusion-reaction model has been widely used to study wildfire dynamics. In this study, we introduce…
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…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
Wildfires represent a problem for ecosystems, human activities, and economies, driven by the climate crisis and land-use changes. Predicting wildfire propagation through mathematical modelling is essential for damage mitigation and risk…
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…
Anthropogenic climate change has increased the probability, severity, and duration of heat waves and droughts, subsequently escalating the risk of wildfires. Mathematical and computational models can enhance our understanding of wildfire…
For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion…
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 analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value.…
We provide a mathematical analysis of a thermo-diffusive combustion model of lean spray flames, for which we prove the existence of travelling waves. In the high activation energy singular limit we show the existence of two distinct…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…
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…
In this paper we consider a classical model of gasless combustion in a one dimensional formulation under the assumption of ignition temperature kinetics. We study the propagation of flame fronts in this model when the initial distribution…
A wildland fire model based on semi-empirical relations for the spread rate of a surface fire and post-frontal heat release is coupled with the Weather Research and Forecasting atmospheric model (WRF). The propagation of the fire front is…
We prove the existence and uniqueness, up to a shift in time, of curved traveling fronts for a reaction-advection-diffusion equation with a combustion-type nonlinearity. The advection is through a shear flow $q$. This analyzes, for…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
Many systems in life sciences have been modeled by reaction-diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events,…