Hyperbolic reaction-diffusion equations for a forest fire model

Abstract

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail. ͓S1063-651X͑97͒02912-7͔

A boundedness-preserving finite-difference scheme for a damped nonlinear wave equation

“…For instance, when the problem under consideration demands the actual measurement of the temperature of a system in Kelvin-as it is the case in the thermodynamical study of the propagation of forest fires [26,27], or in those cases when the variable under study is the size of a biological colony in population dynamics-as in the investigation of the evolution of colonies of parasites [13], or the spread of the human population in Europe during the Neolithic period [9,10]-or in those situations in which the temporal evolution of the concentration of a chemical or biological component in a medium is a characteristic of interest-such as in the analysis of some chemical kinetic systems or in the mathematical modeling of the growth of bacterial films [6]-then the condition of positivity is a qualitative feature that must be maintained.…”

Time-Delayed Theory of the Neolithic Transition in Europe

“…Thus HRD equations, instead of the usual PRD equations, should be regarded as the first choice from a conceptual perspective. Hyperbolic reaction-diffusion equations have been very recently applied to the spread of epidemics [13], forest fire models [14], and chemical systems [15].An interesting application of PRD equations arose after archaeological data led to the conclusion that European farming originated in the Near East, from where it spread across Europe. The rate of this spread was measured [16], and a mathematical model was proposed according to which early farming expanded in the form of a PRD wave of advance [17].…”

“…Thus HRD equations, instead of the usual PRD equations, should be regarded as the first choice from a conceptual perspective. Hyperbolic reaction-diffusion equations have been very recently applied to the spread of epidemics [13], forest fire models [14], and chemical systems [15].…”

Integro-differential models for percutaneous drug absorption

“…Moreover, there is an overestimation of the travelling waves velocity. The drawback observed in equation (3) is also present in the Fisher equation [4][5][6][7][8][9][10] and in the classical heat equation [11][12][13]. In order to overcome these unphysical properties, in the context of the Fisher equation, the flux defined by Fick's law is replaced by a flux with a memory term [4][5][6].…”